Square Root Calculator
Find the square root of a number as a decimal and in simplest radical form, along with its square, cube and cube root.
What is a square root?
The square root of n is the number that, multiplied by itself, gives n. Every positive number has two square roots, one positive and one negative; the symbol √ means the positive one.
Worked example
√50 ≈ 7.0711. Since 50 = 25 × 2 and 25 is a perfect square, √50 = √25 × √2 = 5√2.
Perfect squares
| n | n² | n | n² |
|---|---|---|---|
| 1 | 1 | 9 | 81 |
| 2 | 4 | 10 | 100 |
| 3 | 9 | 11 | 121 |
| 4 | 16 | 12 | 144 |
| 5 | 25 | 13 | 169 |
| 6 | 36 | 14 | 196 |
| 7 | 49 | 15 | 225 |
| 8 | 64 | 20 | 400 |
Frequently asked questions
How do I simplify a square root?
Find the largest perfect square that divides the number, take its root outside, and leave the rest inside: √72 = √36 × √2 = 6√2.
What is the square root of 2?
About 1.41421356. It is irrational, so its decimal never ends or repeats.
Can you take the square root of a negative number?
Not with real numbers. The result is imaginary, for example √−9 = 3i.
How do I estimate a square root by hand?
Find the perfect squares on either side. √50 is between 7 (√49) and 8 (√64), and much closer to 7.
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