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Simplify Radical Calculator: Roots in Simplest Form

This free simplify radical calculator rewrites a root of a whole number in simplest radical form, for example √72 as 6√2 and ∛54 as 3∛2. It shows the prime factors and the decimal value.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

A simplified radical keeps the exact value and removes perfect squares, cubes or higher powers from under the root. Maths classes ask for it in algebra and geometry because it is neater than a long decimal.

Enter a whole number and choose the root.

How to Use This Tool

  1. Enter the value or values asked for in the boxes.
  2. Choose the unit label if there is a choice.
  3. Press Calculate.
  4. Read every result in the table and copy what you need.

How the Calculation Works

The number is factored into primes. For a root of index k, each prime p with exponent e contributes p^floor(e ÷ k) outside the root and p^(e mod k) inside. The outside parts are multiplied into one coefficient and the inside parts into the new radicand.

Worked Example

√72 = 6√2, since 72 = 2³ × 3². ∛54 = 3∛2, since 54 = 2 × 3³. √50 = 5√2 and √49 = 7. √17 stays √17.

Common Uses

  • Algebra and geometry homework.
  • Exact answers in exams.
  • Simplifying formulas.
  • Checking hand work.

Tips and Common Mistakes

  • Only whole numbers are supported.
  • Perfect powers simplify to a whole number.
  • Use a calculator for the decimal value if you need one.
  • Measure carefully: a small error in a length is squared in an area and cubed in a volume, so a 5 percent error in a side can become a 10 percent error in the area or a 15 percent error in the volume.
  • Round only at the end. If you copy a result into another calculation, copy the full number from the tool rather than a rounded one, so small errors do not build up.

Next, you may need the decimal to fraction converter, fraction to decimal converter, system of equations solver, circle calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Taking out of the root every factor that is a perfect power. √72 = √(36 × 2) = 6√2.
It breaks the number into prime factors and takes out one copy for every group of as many equal factors as the root index.
When no prime factor appears as many times as the root index, such as √17 or √30.
Yes. The decimal value is shown only as a check.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.