Square Root Calculator
Find the square root of any number to eight decimal places. For whole numbers the calculator also gives the simplified radical form, such as 6√2 for √72, and tells you whether the number is a perfect square.
- Simplified radical form
- 6√2
- Perfect square?
- No
- The number squared
- 5,184
Saved setups
Save a set of inputs you reuse — your usual rate, your loan, your room sizes — and load it back in one tap.
Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Enter the number.
- Read the decimal square root.
- For a whole number, use the simplified radical form if you need an exact answer.
Worked examples
Square root of 72
- Square root
- 8.48528137
- Simplified radical form
- 6√2
- Perfect square?
- No
Square root of 144
- Square root
- 12
- Simplified radical form
- 12
- Perfect square?
- Yes
Square root of 2
- Square root
- 1.41421356
- Simplified radical form
- √2
Simplifying a square root
Pull out the largest perfect-square factor. 72 = 36 × 2, so √72 = √36 × √2 = 6√2 ≈ 8.4853. If no perfect square other than 1 divides the number, as with √10, it is already in simplest form.
The perfect squares up to 15² are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 and 225.
Two roots, and negative numbers
The equation x² = 49 has two solutions, 7 and −7, but the √ symbol means only the non-negative one, so √49 = 7.
A negative number has no real square root. Its roots are imaginary: √−12 = 2i√3. The calculator shows that simplified imaginary form and leaves the decimal result blank.
Questions people ask
What is the square root of 72?
About 8.4853, or exactly 6√2.
What is the square root of 2?
About 1.41421356. It is irrational, so the decimal never ends or repeats.
Is 144 a perfect square?
Yes. 12 × 12 = 144, so its square root is exactly 12.
Can you take the square root of a negative number?
Not among the real numbers. Using the imaginary unit i, where i² = −1, the square root of −9 is 3i.