Question

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

Answer 1

`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.