Square Root Calculator
Enter a number to get its square root, simplified radical and cube root.
What this tool does
The square root of a number n is the value that multiplied by itself gives n. √72 = 8.48528137, and in simplified radical form 72 = 36 × 2, so √72 = 6√2. √49 is exactly 7 because 49 is a perfect square. Enter a number above.
Calculates the square root and the cube root to many decimal places.
Simplifies the radical and checks for perfect squares.
How to use it
- Enter a number of zero or more.
- Read the square root.
- Read the simplified radical form for whole numbers.
- Check the nearest perfect squares.
Why use this calculator
Gives the square root to eight decimal places, the simplified radical form (72 → 6√2), whether the number is a perfect square and the two perfect squares either side. Maths classes ask for exact radical answers rather than decimals, and finding the largest square factor by hand is fiddly. The calculator shows both forms.
Why we built it
We built the square root calculator to give the simplified radical (72 → 6√2) as well as the decimal, because maths classes ask for exact forms. Use the Pythagorean theorem calculator and the exponent calculator alongside it.
Who this tool is for
- Students learning radicals
- Anyone checking perfect squares
- Builders and DIYers using the Pythagorean theorem
When to use it
- Algebra and geometry homework.
- Checking a Pythagorean calculation.
- Simplifying radicals.
- Finding if a number is a perfect square.
How it works
To simplify √n, factor out the largest perfect square: n = a² × b, so √n = a√b. For 72 = 36 × 2, √72 = 6√2. A perfect square has b = 1. The cube root of n is the number that multiplied by itself three times gives n.
Examples: √50 = 5√2, √49 = 7, √72 = 6√2 ≈ 8.48528137. The cube root of 27 is 3.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Number | 72 |
With those inputs, the calculator returns:
- Square root of 72: 8.48528137
- Simplified radical form: 6√2
- Cube root: 4.160168
- Square: 5,184
- Perfect square: No
- Nearest perfect squares: 8² = 64 and 9² = 81
What you give it, and what you get back
| Item | Details |
|---|---|
| Number | Zero or more; whole numbers get a simplified radical. |
| Output | Square root, simplified radical, cube root, square and nearest perfect squares. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| Negative numbers | Real square roots need zero or more. | The root of a negative number is imaginary: √−n = i√n. |
| Decimal input | A radical form needs a whole number. | The decimal root is still shown. |
| Large numbers | Radicals are computed up to 10^12. | The decimal root is still given. |
Assumptions and limitations
- Real numbers only.
- Radical form for whole numbers up to 10¹².
Frequently asked questions
How do I find a square root?
Find the number that multiplied by itself gives your number, or use the calculator.
How do I simplify a square root?
Factor out the largest perfect square, take its root outside the radical and leave the rest inside.
What is a perfect square?
A whole number that is the square of a whole number, such as 1, 4, 9, 16, 25.
What is the square root of a negative number?
It is imaginary; the calculator works with zero or more.
What is a cube root?
The number that multiplied by itself three times gives the original.
Is my information sent anywhere?
No. The calculation runs in your browser and nothing leaves the page.
Sources and accuracy
The principal square root and the cube root are computed to standard numerical precision, and simplified radicals follow the usual rules for extracting perfect square factors from the radicand.
Figures last checked against the source on . Standards and rates can change — if you are relying on this for something that matters, confirm against the source above. Think a figure is wrong or out of date? Send a correction.