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Calculation Machine

Square Root Calculator

Exact simplified radical plus the decimal value.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Square root
8.48528137
Simplified radical
6√2
Cube root
4.16016765
Square
5184

Working

  1. 1√72 = √(36 × 2) = 6√2

Quick answer

A square root of n is a value that multiplied by itself gives n; non-perfect squares simplify to a radical times an integer.

The formula

√(a²·b) = a√b

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Number72

Result

  • Square root8.48528137
  • Simplified radical6√2
  • Cube root4.16016765
  • Square5184

How to use the Square Root Calculator

  1. 1Enter a number.
  2. 2Read the decimal root.
  3. 3Use the simplified radical for exact answers in algebra.

Frequently asked questions

How do I simplify √72?

Pull out the largest perfect square factor: 72 = 36 × 2, so √72 = 6√2.

Can negative numbers have square roots?

Not in the real numbers. √−9 is 3i in the complex numbers.

About this calculator