Square Root Calculator
Find the square root of any number instantly. Includes nth root, perfect square check, and step-by-step estimation.
How to Use the Square Root Calculator
- Enter any number in the Square Root tab — the result updates instantly as you type.
- See whether the number is a perfect square and its nearest perfect squares above and below.
- Use the Nth Root tab for cube roots, fourth roots, or any other root — enter the number and the root degree.
Formula & Method
The square root of a number x is the value that, multiplied by itself, gives x:
sqrt(x) x sqrt(x) = x
The nth root generalizes this: nth root of x = x^(1/n). Square roots of non-perfect squares are irrational numbers with non-repeating decimal expansions.
Examples
| Number | Square Root | Perfect Square? |
|---|---|---|
| 144 | 12 | Yes |
| 200 | 14.1421356237 | No |
| 625 | 25 | Yes |
| 1000 | 31.6227766017 | No |
| 1024 | 32 | Yes |
Frequently Asked Questions
What is a square root?
The square root of a number is the value that, when multiplied by itself, equals the original number. For example, the square root of 25 is 5 because 5 x 5 = 25.
What is a perfect square?
A perfect square is a number whose square root is a whole number, like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
Can you take the square root of a negative number?
Not in real numbers. The square root of a negative number is imaginary — for example, sqrt(-9) = 3i, where i is the imaginary unit.
How do I estimate a square root manually?
Find the two perfect squares it sits between. For sqrt(50): 49 (7^2) and 64 (8^2), so the answer is between 7 and 8, closer to 7. Actual: 7.071.
What is the square root of 2?
The square root of 2 is approximately 1.4142135624. It is an irrational number, meaning its decimal expansion never ends or repeats.
People Also Ask
What is the square root of 144?
The square root of 144 is exactly 12, because 12 x 12 = 144. 144 is a perfect square.
How do you find the square root without a calculator?
Use the guess-and-check method: estimate, square your guess, then refine. For sqrt(200): 14^2 = 196 (too low), 14.2^2 = 201.64 (too high), 14.14^2 = 199.94 — so sqrt(200) is about 14.14.
Is the square root of a number always smaller?
For numbers greater than 1, yes. For numbers between 0 and 1, the square root is actually larger — for example, sqrt(0.25) = 0.5.