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

##= color(blue)(9/4##

##sqrt (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##