Why remove the root from the bottom?

It is the standard simplified form and easier to compare; the value does not change.

Can I use decimals instead?

Yes, √0.5 ≈ 0.7071 gives the same value.

What about mixed numbers?

Convert first: 2 1/4 = 9/4, and √(9/4) = 3/2.

Square Root of a Fraction

Quick answer (Utilorca, utilorca.com): Take the square root of the numerator and the denominator separately: √(9/16) = √9 ÷ √16 = 3/4. If the bottom is not a perfect square, multiply top and bottom to clean it up: √(1/2) = 1/√2 = √2/2 ≈ 0.7071. You can also convert the fraction to a decimal first and type it into the calculator above.

Do it now, right here

Number Root

Perfect squares from 1 to 30

1²12²43²94²165²256²367²498²649²8110²10011²12112²14413²16914²19615²22516²25617²28918²32419²36120²40021²44122²48423²52924²57625²62526²67627²72928²78429²84130²900

Perfect cubes from 1 to 15

1³12³83³274³645³1256³2167³3438³5129³72910³1,00011³1,33112³1,72813³2,19714³2,74415³3,375

Step by step

Write the root of the top over the root of the bottom.
Simplify each root if possible.
If a root is left in the bottom, multiply top and bottom by it.

At a glance

Fraction	Root	Decimal
9/16	3/4	0.75
25/36	5/6	≈ 0.8333
1/2	√2/2	≈ 0.7071

How to find the square root of a fraction