Math

Square Root Calculator

Exact simplified radical plus the decimal value.

Enter your values

Enter the number you are working with.

Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.

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.

√(a²·b) = a√b

At a glance

What it doesExact simplified radical plus the decimal value.
CategoryMath
Inputs neededNumber
Main outputSquare root
Formula√(a²·b) = a√b
CostFree — no sign-up, no download

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.

Inputs explained

Number
Enter the number you are working with.

Worked example

Using the values the calculator loads with:

Inputs

  • Number72

Results

  • Square root8.48528137
  • Simplified radical6√2
  • Cube root4.16016765
  • Square5184
  1. √72 = √(36 × 2) = 6√2

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.

What do I need to enter into the Square Root Calculator?

Just 1 value: number. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.

How does the Square Root Calculator work out the 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. It applies the formula √(a²·b) = a√b and shows the working so you can check each step by hand.

Is the Square Root Calculator free, and do I need an account?

It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.

Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.