Question

How do you simplify `sqrt10 times sqrt6`?

Answer 1

`2sqrt15`

Explanation:

using the following facts about radicals:

`sqrta xxsqrtb = sqrtab hArr sqrtab = sqrta xx sqrtb`

and `sqrta xx sqrta = a`

look for the factors of 10 and 6 , particularly 'squares'

factors of 10 are 1,2,5,10 and factors of 6 are 1,2,3,6 . Apart from 1 there are no squares and so

`sqrt10 =sqrt2 xxsqrt5 color(black)(" and ") sqrt6 = sqrt2 xxsqrt3`

`rArr sqrt10 xxsqrt6 = sqrt2 xxsqrt2 xxsqrt3 xxsqrt5`

using the above facts simplifies to `2sqrt15`