How do you find the square root of 92/207?

1 Answer
Feb 5, 2017

Answer:

#sqrt(92/207) = 2/3#

Explanation:

First check the prime factorisations of the numerator and denominator to see what square factors there are:

#92 = 2 * 2 * 23#

#207 = 3* 3 * 23#

So:

#sqrt(92/207) = sqrt((2^2*color(red)(cancel(color(black)(23))))/(3^2*color(red)(cancel(color(black)(23))))) = 2/3#

Note that #92/207# has another square root, namely #-2/3#, but I follow the common usage here that "the" square root means the non-negative one.