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How to Get Square Root of Fractions with Calculator

Reviewed by Calculator Editorial Team

Calculating the square root of fractions is a common mathematical operation that appears in algebra, geometry, and many practical applications. This guide explains how to perform this calculation using both a calculator and manual methods, with clear examples and practical tips.

How to Calculate Square Root of Fractions

The square root of a fraction is the square root of the numerator divided by the square root of the denominator. This can be expressed mathematically as:

√(a/b) = √a / √b

Where:

  • a is the numerator
  • b is the denominator

This property allows you to simplify the calculation by taking the square root of the numerator and denominator separately.

Important Note

Remember that the square root of a fraction is not the same as the fraction of square roots. The correct approach is to take the square root of the entire fraction, not the square roots of the numerator and denominator separately unless you're simplifying.

Using a Calculator

Most scientific calculators have a square root function that can handle fractions. Here's how to use it:

  1. Enter the numerator of your fraction
  2. Press the division key (÷)
  3. Enter the denominator of your fraction
  4. Press the square root key (√)

For example, to calculate √(4/9):

  1. Enter 4
  2. Press ÷
  3. Enter 9
  4. Press √

The calculator will display the result as 2/3.

Tip

If your calculator doesn't directly support fractions, you can enter them as decimals and then convert the result back to a fraction if needed.

Manual Calculation Method

If you need to calculate the square root of a fraction manually, follow these steps:

  1. Take the square root of the numerator
  2. Take the square root of the denominator
  3. Divide the result from step 1 by the result from step 2

For example, to calculate √(16/25):

  1. √16 = 4
  2. √25 = 5
  3. 4 ÷ 5 = 0.8

The result is 0.8, which is equivalent to 4/5.

Simplification

After calculating, simplify the resulting fraction if possible. For example, √(9/16) = 3/4 is already in simplest form.

Worked Examples

Example 1: Simple Fraction

Calculate √(4/9):

  1. √4 = 2
  2. √9 = 3
  3. 2 ÷ 3 = 0.666... or 2/3

Result: 2/3

Example 2: Complex Fraction

Calculate √(16/25):

  1. √16 = 4
  2. √25 = 5
  3. 4 ÷ 5 = 0.8 or 4/5

Result: 4/5

Example 3: Mixed Numbers

Calculate √(3/12):

  1. Simplify the fraction first: 3/12 = 1/4
  2. √1 = 1
  3. √4 = 2
  4. 1 ÷ 2 = 0.5 or 1/2

Result: 1/2

FAQ

Can I calculate the square root of a fraction with a basic calculator?
Yes, you can enter the fraction as a decimal and then take the square root. For example, √(1/4) = √0.25 = 0.5.
What if the numerator or denominator isn't a perfect square?
The result will be an irrational number. For example, √(2/3) ≈ 0.8165. You can leave it as a decimal or express it as a simplified radical: √(2/3) = √6 / 3.
How do I simplify the result of a square root of a fraction?
After calculating, check if both the numerator and denominator can be simplified. For example, √(8/18) = √(4/9) = 2/3.
Can I use this method for negative fractions?
No, the square root of a negative number is not a real number. Fractions with negative numerators or denominators require imaginary numbers.