Fraction Square Root Calculator

Enter fractions, mixed numbers, and precision settings. See exact radicals, decimals, checks, and visual summaries. Download reports, inspect examples, and solve fraction roots confidently.

Calculator Form

Whole Part (optional)

Use this for mixed numbers like 1 3/4.

Numerator

For mixed numbers, keep this positive.

Denominator

The denominator must be greater than zero.

Decimal Precision

Choose between 2 and 12 decimal places.

Advanced Display

Show factor breakdown

Show rationalized exact form

Actions

Example Data Table

Input	Simplified Fraction	Exact Root	Decimal Root
1/4	1/4	1/2	0.5
2/3	2/3	√6/3	0.816497
9/16	9/16	3/4	0.75
1 7/9	16/9	4/3	1.333333
5/12	5/12	√15/6	0.645497

Formula Used

1) Convert a mixed number to an improper fraction
If the input is w n/d, then the improper numerator becomes:
(|w| × d + n), with the sign taken from the whole part.

2) Square root of a fraction
For a positive fraction a/b:
√(a/b) = √a / √b

3) Simplify by extracting perfect squares
Write the numerator and denominator as:
a = s² × r and b = t² × u
Then:
√(a/b) = (s/t)√(r/u)

4) Rationalized form when needed
If the radical still contains a denominator, multiply top and bottom by √u:
(s/t)√(r/u) = s√(ru)/(tu)

5) Decimal check
After computing the root numerically:
check = (√(a/b))²
The check should match the original fraction value within rounding tolerance.

How to Use This Calculator

Enter a whole part only when your value is a mixed number. Leave it as zero for an ordinary fraction.

Type the numerator and denominator, then choose the number of decimal places you want in the result.

Enable the factor breakdown option if you want to see how the calculator extracts perfect square factors from the fraction.

Enable the rationalized form option when you want the exact answer with a rational denominator.

Press the calculate button. The result appears above the form and below the header, along with the chart and export tools.

FAQs

1) Can this calculator handle mixed numbers?

Yes. Enter the whole part, numerator, and denominator. The calculator converts the mixed number into an improper fraction before finding the square root and simplifying the result.

2) Does the calculator simplify radicals?

Yes. It extracts perfect square factors from the numerator and denominator, then presents the exact simplified radical form whenever the square root is not a clean rational number.

3) What happens if the fraction is already a perfect square?

The exact result becomes a rational value such as 3/4 or 2. The decimal result is also shown using the precision you selected.

4) Can it solve negative fractions?

This page is limited to real square roots. Negative fractions would produce imaginary values, so the calculator shows a notice instead of a real-number result.

5) Why is a rationalized form useful?

A rationalized form removes radicals from the denominator. Many textbooks, exams, and engineering workflows prefer that style because it is easier to compare and standardize.

6) Does the decimal value exactly match the exact form?

Yes, within rounding. The decimal output is a rounded approximation of the exact radical expression, and the squared check helps verify the original fraction value.

7) What does the factor breakdown show?

It shows how the numerator and denominator are written as a perfect square times a remaining factor. That makes the simplification process transparent and easier to follow.

8) What do the CSV and PDF downloads include?

The CSV export saves calculation history in table form. The PDF button creates a compact summary report of the current result and the recent stored calculations.