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`