Fraction Root Calculator

Enter a fraction, select the root degree, and quickly calculate the result.

Calculate Roots of Fractions

Fraction
Result

What Is a Fraction?

A fraction is a number composed of two integers, usually written as \( \frac{a}{b} \), where \( a \) is the numerator and \( b \) is the denominator. A mixed number is a number made up of an integer part and a regular fraction, such as \( 1 \frac{1}{2} \).

How to Calculate the Root of a Fraction?

Given a fraction and the root degree, the calculation steps are as follows:

  1. Identify the Fraction and Root Degree: Let the fraction be \( \frac{a}{b} \) (which can be either a regular fraction or a mixed number) and the root degree be \( n \).
  2. Convert Mixed Number to Improper Fraction (if applicable): If a mixed number is entered, first convert it to an improper fraction. For example, \( 1 \frac{1}{2} = \frac{3}{2} \).
  3. Apply the Root Formula: The formula for calculating the root of a fraction is: \( x = \sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}} \)

Examples

Example 1: Calculate the square root of \(\frac{16}{9}\)

Solution:

Compute:

\( x = \sqrt[2]{\frac{16}{9}} = \frac{\sqrt{16}}{\sqrt{9}} = \frac{4}{3} \)

Conclusion: The square root of \( \frac{16}{9} \) is \( \frac{4}{3} \).

Example 2: Calculate the cube root of \( \frac{27}{64} \)

Solution:

Compute:

\( x = \sqrt[3]{\frac{27}{64}} = \frac{\sqrt[3]{27}}{\sqrt[3]{64}} = \frac{3}{4} \)

Conclusion: The cube root of \( \frac{27}{64} \) is \( \frac{3}{4} \).

Example 3: Calculate the square root of \( 2 \frac{1}{4} \)

Solution:

Convert the mixed number to an improper fraction:

\( 2 \frac{1}{4} = \frac{9}{4} \)

Compute:

\( x = \sqrt[2]{\frac{9}{4}} = \frac{\sqrt{9}}{\sqrt{4}} = \frac{3}{2} \)

Conclusion: The square root of \( 2 \frac{1}{4} \) is \( \frac{3}{2} \).