How do you simplify #sqrt21/sqrt15#?

1 Answer
Sep 9, 2016

Answer:

#sqrt(7/5) = sqrt35/5#

It is debatable which one would be considered "simpler'

Explanation:

Two square roots being divided can be combined into one:

#sqrt21/sqrt15 = sqrt(21/15)" "larr# this can be simplified.

#sqrt(21/15) = sqrt((cancel3xx7)/(cancel3xx5))#

=#sqrt(7/5)#

It is possible then to rationalise the denominator

#sqrt(7/5) = sqrt7/sqrt5 xx sqrt5/sqrt5#

=#sqrt35/5#