What is sqrt(27/16)?

2 Answers
Jul 26, 2015

I found: 3/4sqrt(3)

Explanation:

You can write your square root as:
sqrt(27)/sqrt(16)=sqrt(3*9)/4=(sqrt(9)sqrt(3))/4=3/4sqrt(3)

Jul 26, 2015

(3sqrt(3))/4

Explanation:

Use the quotient property of radicals to rewrite your expression as

sqrt(27/16) = sqrt(27)/sqrt(16) = sqrt(27)/4

Since 27 is not a perfect square, you're going to have to see if you can write it as a product of a perfect square and another number

27 = 9 * 3 = 3^2 * 3

This means that your expression will be

sqrt(3^2 * 3)/4 = (sqrt(3^2) * sqrt(3))/4 = color(green)((3 sqrt(3))/4)