Radical Times a Radical Math

Introduction to radical times a radical math:
Radicals are nothing but a root which we also called as square root. Square root is indicated with the symbol (sqrt) and sqrt (). Normally, radicals are rewrite like; sqrt of (b) is rewrite as `b ^(1/2)` . Likewise radicals are expressed in various forms. The expression `sqrt (8)` is read as “radical eight”, or “the square root of eight”. Thus, we are going to discuss about the radical times radical in math which related to multiplication of two radicals in math.

Radical Times a Radical Math:

Radical times a radical is nothing but multiplying a radical with another radical in math. This is similar to the normal multiplication of radicals in math.

General expression with exponent and radical:

`n (sqrt (a)) ^m =(n (sqrt (a))) ^m =(a1/n) ^m = a^m/n`                  

Multiplication property for radical expression: `n (sqrt (ab)) = n (sqrt (a)) n (sqrt (b))`

Division property for radical expression: `n (sqrt (a/b)) = (n (sqrt (a))) / (n (sqrt (b)))`

From, the above properties, we are going to learn about multiplication property in math is like,

`sqrt (a) xx sqrt (b) = sqrt (ab)`

Example for Radical Times a Radical Math:

Example for radical times radical math 1: Multiply the given radicals:  (2`sqrt 4` ) × (`root(2)(16)` )

(2`sqrt4` )  (`root(2)(16)` ) =2 × 2 × (`root(2)(16)` )

=2 × 2 × 4

=16

Answer: `16`

Example for radical times radical math 2: Multiplying the given radicals: (`sqrt (3)` ) (5`sqrt(5)` )

`sqrt (3)`.   (5`sqrt(9)` ) = `5``sqrt(3 xx 5)`

=`5sqrt(15)`

Answer: `5sqrt(5)`

Example for radical times radical math 3: Multiply the given radicals:   ( ` sqrt( 8)` ) `7sqrt(15)`

( ` sqrt( 8)` ) (`7` `sqrt(15)` )   = `sqrt(2 xx 4)` . `7` `sqrt(15)`

= `2``sqrt( 2)` `xx ` `7``sqrt(15)`

= `14` ` sqrt(30)`

Answer: `14sqrt (30)`

Example for radical times radical math 4: Multiply radicals:  `sqrt 16 and sqrt 81`

(`sqrt(16)` ) (`sqrt(81)`) =`sqrt(16)` `sqrt(81)`

= `sqrt(4 xx 4 xx 9 xx 9)`

= `4 xx 9`

= `36`

Answer: `36`

Post a Math Problem

Introduction to post a math problem:

Post a math problem is that several math problem posted on the internet for the students help. There are many websites that post a math problems to help the students. Among the entire website tutor vista is the famous and wonderful website which has excellent tutoring team to help the students any time with all the homework problems. The tutoring team will be online 24 x 7 to help the students.In the tutor vista website any student can post a math problem at any time and they can immediately get help. In this article let us see sample math problems posted in this website.

Post a Math Problem:

Example 1:

Find the solution of p in the equation 7p + 4p = 55

Solution

Given equation is 7p + 4 p = 55

Add leht side of the equation since both are in terms of p

7p+ 4p = 55 p

So 11p = 55

Divide both sides by 11

`(11p)/11` = `55/11`

p = 5.

Check the value by substituting p = 5 in the given equation

7(5)+4(5) = 55

35 + 20 = 55

55 = 55

So the answer p = 5 is correct.

Example 2:

Solve for x in the given equation 10x + 2 = 47

Solution

The given equation is 10x+2 = 47

Subtract 2 on both sides

So 10x + 2 -2 = 47 - 2

By subtracting 2 the equation is formed as 10x = 45

Now divide by 10 on both sides

`(10x)/10` = `45/10`

x = 4.5

So we get the answer as x = 4.5.

Now we can check this whether our answer is correct or not. For checking our answer substitute the value x = 4.5 in the given equation at the place of x

So given equation is 10x + 2 = 47

Substitute x = 4.5

10(4.5) + 2 = 47

45 + 2 = 47

47 = 47

So both sides are equal and our answer x = 4.5 is correct.

Post a Math Problem:

Here are some of the question. Solve and find out the solution and check as shown above.

1. Find the value of k of the equation 3k = 27

2. Find the value of p of the equation 8p - 3p = 75

3. Find the value of p of the equation 12 p = 42 + 102

4. Find the value of m of the equation 15m - 7m = 2m +66

5. Find the value of s of the equation 5s + 50 - 3s = 60

Answers

1. k = 9

2. p = 15

3. p = 12

4. m =11

5. s = 5

Easy Way to Simplify Fractions

Introduction:

   These articles we are discuss about simplify fractions in easy way. A fraction is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (`1/2` , `5/8` , `3/4` etc.) and which consist of a numerator and a denominator. (Source – Wikipedia)

Easy way to simplify fractions solves the simple addition fraction, multiplication fraction and subtraction fraction.

Easy Way to Simplify Fractions-example Problems:

Example 1:

Add the fractions for given two fraction, `2/5` + `1/5`

Solution:

The given two fractions are `2/5` + `1/5`

The same denominators of the two fractions, so

                                         = `2/5` + `1/5`

Add the numerators the 2 and 1 = 2+1 = 3.

The same denominator is 5.

                                         = `3/5`

The addition fraction solution is `3/5` .

Example 2:

Subtract the fractions for given two fraction `4/6` - `3/3`

Solution:

The denominator is different so we take a (lcd) least common denominator

LCD = 6 x 3 = 18

So multiply and divide by 3 in first term we get

                                                           `(4 xx 3) / (6 xx 3)`

                                                         =`12/18`

Multiply and divide by 6 in second terms

                                                        = `(3 xx 6) / (3 xx 6)`

                                                       = `18/18`

The denominators are equals

So subtracting the numerator directly = `(12-18)/18`

Simplify the above equation we get = `-6/18`

Therefore the final answer is `-1/3`

Example 3:

Multiply the fractions for given two fraction, `4/6` x `5/6`

Solution:

The given two fractions are `4/6 ` x `5/6`

The same denominators of the two fractions, so

                                         = `4/6` x `5/6`

Multiply the numerators the 4 and 5 = 4 x 5 = 20.

Multiply the denominators the 6 and 6 = 6 x 6= 36

                                         =` 20/36`

The multiply fraction solution is `5/9`

Example 4:

Dividing fraction:

`5/7 ` divides `2/4`

Solution:

First we have to take the reciprocal of the second number

Reciprocal of `2/4` = `4/2`

Now we multiply with first term we get

`5/7` x `4/2`

Multiply the numerator and denominator

`(5 xx 4) / (7 xx 2)`

Simplify the above equation we get

= `20/14`

Therefore the final answer is `10/7`


Easy Way to Simplify Fractions-practice Problems:

Problem 1: Add the two fraction `3/9` + `2/9`

Solution: `5/9`

Problem 2: Subtract two fractions `10/9` – `6/9`

Solution: `4/9`

Problem 3: multiply two fractions `6/5` x `6/6`

Solution: `6/5`

Problem 4: Dividing two fractions `5/6` and `2/4`

Solution:` 5/3`

Solving Calculus Math Problem

Introduction to solving calculus math problem:
There are various branches exist in mathematics. The calculus is an important part of mathematics. It deals with the limits, functions, derivatives, integrals, and infinite series. In general calculus is divided into two parts,they are differential and integral calculus. Now we are going to discuss various problems related to calculus.

Example Problems for Solving Calculus Math Problem:

Solving calculus math problem – Example: 1

Solve `\int x^2e^xdx`

Solution:

Both side integration by the parts of twice to get this to an integral for which we know the formula.

`u=x^2`

`du=2xdx`

`dv=e^xdx`

`v=e^x`

`\int x^2e^xdx=x^2e^x-2\int xe^xdx`

`u=x`

`du=dx`

`dv=e^xdx`

`v=e^x`

`\int x^2e^x=x^2e^x-2\[xe^x-\int e^xdx\]=x^2e^x-2xe^x+2e^x+C`

Solving calculus math problem – Example: 2

Solve `\int \frac{\sqrt{x^2-4}}{x}dx`

Solution:

`x=2\sec \theta`

`dx=2\sec \theta\tan \thetad\theta`

`\int \frac{\sqrt{x^2-1}}{x}dx=\int \frac{\sqrt{4\sec^2\theta-4}}{2\sec \theta}(2)\sec \theta\tan \thetad\theta=2\int \sqrt{\tan^2\theta}\tan \thetad\theta=2\int \tan^2\thetad\theta`

We must use a trig substitution to get this in a form that is more easily integrable.

`2\int \tan^2\thetad\theta=2\int (\sec^2\theta-1)d\theta=2[\tan \theta-\theta]+C`

Now, we know `\sec \theta=\frac{x}{2} so \tan \theta=\frac{\sqrt{x^2-4}}{2} and \theta=\arcsec \frac{x}{2}.` So

`\int \frac{\sqrt{x^2-4}}{x}dx=2\ [\frac{\sqrt{x^2-4}}{2}-\arcsec \frac{x}{2}\ ]+C=\sqrt{x^2-4}-2\arcsec \frac{x}{2}+C`

Practice Problems for Solving Calculus Math Problem:

1. Solve `\int_0^\infty x^4 e^{-x^3} dx`

`Answer: \frac{2}{9}\Gamma\(\frac{2}{3}\)`

2. Simplify `\int_0^\infty 3^{-4z^2}dz`

`Answer: \sqrt{\frac{\pi}{16\ln3}}`

Consonant Math Definition

Introduction to consonant math definition
Let us discuss about the consonant math definition. The necessary of mathematics learn to the measurement, arrangement, space and modify. The consonant is called as they do not change the number. The consonant math is defined the fixed value of a problem. The example of the fixed value is maximum value of amount, minimum value of amount, dates, cost, title lines error messages. The consonant math numbers normally declare only real number does not used the imaginary numbers. Next we see the consonant math definition.

Consonant Math Definition

The addition math definitions are calculate the total value otherwise sum of the values. There are combine the many numbers. The addition example is 8+1+2=11. The addend are declare the any number, that is 8, 1, and 2 are addend.

The subtract math definitions are single value away from other value. The example is the value is 8 that are subtracting the 5, the answer is 3. The symbol is 8 - 5 = 3.

The multiplication math definitions are calculated the multiplying by the repeated value in addition. The example of multiplication is 4 x 2 = 4 + 4 = 8.

The math definitions of division are splitting into the same parts otherwise groups. The example is the 18 is divided the 3. The division answer is 6.

The math definitions of polygon is the many occurring similar line, all connected to the closed shape in the end to end format.

Other Consonant Math Definitions

The definition of circle is drawing the curve is always the similar distance of the curve, the line from the middle of circle to a position on the circle.

The definition of triangle is the two sides are same in the triangle length. The properties of triangle are vertex, area, and median. Scalene triangle is define the all sides are not equal.

The math definitions are square is each sides are same and to the every internal angels in 90o. The square is simply specified the regular polygon.

Variability in Math

Introduction to variability in math:

In statistics math, variability or variation is nothing but the spread in a variable. Some of the common measures of variability in statistics math are range, variation, and standard deviation. In this article variability in math , we are going to discuss about finding the measures of variability through the example problems, which will be very useful for the math students.

Measures of Variability - Range:

Definition:

Range is the difference between a greater value and a smaller value.

Steps involved to learn range:

Step 1: Arrange the given numbers from ascending to descending order.

Step 2: Identify the larger value in the set of data

Step 3: Identify the smaller value in the set of data

Step 4: We have to find the difference between larger and smaller value.

Example problems:

Example 1:

Find the range for the following set of data:

{ 13 , 14 , 15 , 16 , 17 }

Solution:

Range   =  larger value - smaller value

=  17 - 13

=  4

Example 2:

Find the range for the following set of data:

{ 8 , 14 , 24 , 34 , 45 }

Solution:

Range   =  larger value - smaller value

=  45 - 8

=  37

Measures of Variability - Variance and Standard Deviation:

Definition:

Variance is the mean of the squared deviation from its expected value. The standard deviation is the square root of its variance.

Step-by-step explanation:

Step 1: Mean:Find the average or mean value of the given data

Step 2: Variance:To find the variance, get each difference from the mean value and square the each value and finally

average the result.

Step 3: Standard deviation: Find the square root of variance to calculate the standard deviation.

Example problem:

Find the variance and standard deviation for the given set of data:

{ 2, 9, 3, 1, 5 }

Solution:

Step 1: Mean

Mean   =  ` ( 2 + 9 + 3 + 1 + 5 ) / 5`

=  ` 20 / 5`

= 4

Step 2: Variance

Variance  =   `( (5-4)^2 + (9-4)^2 + (3-4)^2 + (1-4)^2 + (5-4)^2 )/5`

=   `( (1)^2 + (5)^2 + (-1)^2 + (-3)^2 + (1)^2 )/5`

=   `(1+25+1+9 + 1)/5`

=   `37/5`

=  7.4

Step 3:Standard deviation

Standard deviation  =  `sqrt ( 7.4 )`

=  2.72

Rules Algebraic Expressions

Introduction :

In mathematics, an expression is a finite combination of symbols that are well formed according to the rules applicable in the context at hand. Symbols can designate values (constants), variables, operations, relations, or can constitute punctuation or other syntactic entities. The use of expressions can range from simple arithmetic operations like

`3+5 xx ((-2)^(7)- (3)/(2))`

Source: Wikipedia

Looking out for more help on Significant Figures Rules in algebra by visiting listed websites.

Rules for Solving Algebraic Expressions:

Step 1: Group the terms containing the identical variable collectively in algebraic expressions.

Step 2: carry out the operation inside the parentheses for the variable and other.

Step 3: revise the algebra 2 simplify expressions and solving algebraic expressions.

Step 4: To make sure the equation, if there is able to simplify the algebraic simplify expressions and then repeat the step 1 to 4.

Example problems for solving algebraic expressions using rules:

Solving algebraic expressions using rules, 12x+5y+10+10z-3y+6x+10z-2

Solution:

Step 1: Is to group like terms. Group the terms containing the same variable together. Group constants together.

(12x+6x)+(5y-3y)+(10z+10z)+(10-2)

Step 2: Is to carry out the operation inside the parentheses for the variable x.

(12x+6x)=18`xx` x= 18x

Step 3: Is to carry out the operation inside the parentheses for the variable y.

(5y-3y)=2y

Step 4: Is to carry out the operation inside the parentheses for the variable z.

(10z+10z)=20z

Step 5: Is to carry out the operation inside the parentheses for the constants.

10-2=8

Step 6: Is to revise the problem.

18x+2y+20z+8

Since the left over terms are not like terms, the problem cannot be any further.

The correct answer is 18x+2y+20z+8

My forthcoming post is on how to solve an algebraic expression, free algebra 2 solver will give you more understanding about Algebra.

Rules for Solving Algebraic Expressions in Order of Operation:

In long math problems with +,-,x,%,(), and exponents in them, you have to identify what to do first. Without follow the same rules, you may get unlike answers. You can easily keep in mind the silly sentence, Big Elephants Destroy Mice And Snails, you can commit to memory the order of operations, and you must follow.

Big                   “B” means Brackets. We need to carry out operation in side parentheses first. 

Elephants          “E” means an exponent, you must calculate exponents next.

Destroy            “D” means division. Begin on the left of the equation and perform all multiplication and divisions in the order in which they appear.

Mice                “M” means multiply

And                 “A” means addition.

Snails              “S” means subtract. For all time on the left hand side and carry out additions and subtractions operation.

Example for solving algebraic expressions using order of operations rules:

To solving 16`-:`4(2-5)+5-2 using order of operations rules in algebra.

Solution:

=16`-:`4(2-5)+5-2

=16`-:`4(-3)+5-2   where 16`-:`4 are `16/4`

=`16/4` `xx`(-3)+5-2

=4`xx`-3+5-2

=-12+5-2

=-7-2

=-9

Answer is -9

Probability Number Line

Definition of probability number line:
The probability number line is one of the major topics in mathematics. Probability number line determines how likely some event will be happening. Probability distribution is consists the list of all the number random variables and their corresponding probabilities.To valid probability must be 0 and 1. And sums of probability number must be equal to 1.

P (A) =n/N

n specifies occurrence event of A

Example of Intersection Probability Number Line :

The reverse or set off an occurrence event A is the occurrence events of not A. It specifies the event A not occurring.

So mathematical expression of probability is given by P (not A) = `1 - P (A).`

An example probability of not rolled a 6 on a 6side die is [1 – (possibility of rising and falling a six)].

So probability is=1-1/6

Answer=5/6

Join probability:

Consider A and B are Events. In this A and B are occur in a single experiments are called as the Join probability. Join probability is some time called as intersection probability. That is denoted as `P (AnnB).` Suppose A and B are not depending means join probability is given in below

`P (A and B) =P (AnB) =P (A) P (B)`

The given probable sums are example for intersection probability.

The 2 coins are tossed. The probability number line for both coin get Heads=1/2*1/2

The Answer is=1/4

If flipping a single coin 3 times means find the probability number line

If 3 times flipping then probabilities are

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

Events are

M =Head on first flip, N =Tails on First Flip, O=Heads on Second flip

S=Three heads, Q=Three Tails, R=zero Heads
Probability number lines are

Between, if you have problem on these topics all prime numbers from 1 to 100, please browse expert math related websites for more help on the prime number theorem.

Example for Union Probability:

Suppose the A event or B event or both events occurred in first time of an experiment that is called as union of events. The union events A and B denoted as P(AUB). If two events are commonly selected then the probability is

`P (A or B) =P (AuuB) =P (A) +P (B)`

The given probable sums is the chance for rolling a die is 1 or 2 on a six-sided die is

`P (A or B) =P (A) +P (B)`

`P (1 or 2) =P (1) +P (2)`

`P(1)=1/6 and p(2)=1/6`

`=1/6+1/6`

`Answer is=1/3`

Find probability for even number obtain when a die was rolled.

Identify the sample space values that is s and number line are given below

`S= {1, 2, 3, 4, 5, 6}`

Write only the even number line in S

`E= {2, 4, 6}`

Use Classical probability formula

`P (E) = n (E) / n(S)`

`P (E) = 3 / 6`

`P (E) = 1 / 2`

Ordered Pair Math

Introduction to ordered pair math:

An ordered pair in math is the pair of two objects which occur in a particular order.

That is, here that order is very important.

Ex: Let 7 and 9 be two numbers. Then (7, 9) is one ordered pair and (9, 7) is another ordered pair. Hence in (7, 9) we call 7 as the first component and 9 as the second component.

Two ordered pairs are said to be equal if they have the same first components and the same second components.

Ex: (- 7, 11) = (- 7, 11) and (5, 8) = (5, 8).

Suppose (x, y) = (4, 3). Then x = 4, y =3.

Now let us see few problems on these concepts.

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Example Problems on Ordered Pair Math:

Ex 1: By using the set A = {a, b}, form all possible ordered pairs.

Solution: Given:  A = {a, b}.

Therefore the ordered pairs are {(a, a), (a, b), (b, a), (b, b)}.

Ex 2: Find all possible ordered pair from X = {1, 2, 3}.

Solution: Given: X = {1, 2, 3}.

Therefore the possible ordered pairs are given by { (1,1), (1,2 ), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3) }

Ex 3: If (3a – 5, 8b +7) = (7, 23), Find the value of ‘a’ and ‘b’.

Solution: Given: (3a – 5, 8b +7) = (7, 23)

`implies` 3a -5 = 7 and 8b + 7 = 23

`implies` 3a = 5+7 and 8b = 23 – 7

`implies ` 3a = 12 and 8b = 16

`implies` a = `12/3` = 4 and b = `16/8` = 2.

Therefore a = 4 and b = 2.

Ex 4: If (3a, - 5) = (a -2, b+3), find the values of ‘a’ and ‘b’.

Solution: Given: (3a, -5) = (a- 2, b+3)

`implies` 3a = a – 2 and -5 = b+3

`implies ` 3a – a = - 2   and -5 – 3 = b

`implies` 2a = - 2   and b = - 8

`implies` a = `-2/2` = - 1 and b = -8.

Therefore a = -1, b = - 8.

Practice Problems on Ordered Pair Math:

1. If (x – 3, x + 2y) = (3x -1, 3), Find the value of x and y.

[Ans: x = -1, y = 5/2]

2. If (3a – 2) 5 – b) = (4, - 1), find a and b.

[Ans: a = 2, b = 6].