How do you simplify #sqrt10 times sqrt6#?

1 Answer
Feb 4, 2016

Answer:

# 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#