# How do you find the square root of 81/16?

Jun 7, 2016

= color(blue)(9/4

#### Explanation:

$\sqrt{\frac{81}{16}}$

We simplify $81$ and $16$ by prime factorisation (expressing a number as a product of its prime factors).

• sqrt (81) = sqrt (3 * 3 * 3 * 3 ) = sqrt ( 9 * 9 ) = sqrt (9^2) = color(blue)(9

• sqrt (16) = sqrt (2 * 2 * 2 * 2 ) = sqrt ( 4 * 4 ) = sqrt (4^2) = color(blue)(4

So, sqrt (81/16) = color(blue)(9/4