Square Root Calculator
Calculate square roots, cube roots, and check for perfect squares.
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Quick Tip
Enter the number you want the root of.
About This Tool
Why use Square Root Calculator?
This calculator returns the square root of a number, its cube root and its square, and tells you whether the number is a perfect square. The square root of x is the value that, multiplied by itself, gives x: √144 = 12 because 12 × 12 = 144.
Perfect squares are the whole numbers with whole-number roots: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 and so on. Every other positive number has an irrational root that never ends or repeats, so the result here is rounded for display. Negative numbers have no real square root, which is why the tool works from the absolute value; their roots are imaginary.
Key Benefits
Square root, cube root and square
Three related results on one screen, so you can check an answer by squaring it again.
Perfect square detection
Tells you immediately whether the number has an exact whole-number root, which is what most homework questions are testing.
Works with decimals
Roots of decimals and large values are handled the same way, with results rounded for readability.
How to use Square Root Calculator
- 1
Enter the number you want the root of.
- 2
Read the square root, and check the perfect-square indicator to see whether the answer is exact.
- 3
Compare with the cube root, which is the number that gives your value when multiplied by itself three times.
- 4
Use the squared value to work backwards and confirm the result.
Best use cases
Check homework answers on roots and perfect squares.
Find the side length of a square from its area.
Work out the distance term in the Pythagorean theorem.
Convert a variance into a standard deviation.
Square Root Calculator FAQs
What is a perfect square?
A number whose square root is a whole number, such as 49 (7 × 7) or 225 (15 × 15). Numbers like 50 are not perfect squares, so their roots are irrational decimals.
Can you take the square root of a negative number?
Not within the real numbers, because any real number multiplied by itself is positive. Mathematicians define √−1 as the imaginary unit i, so √−9 = 3i. This calculator works from the absolute value instead.
What is the difference between a square root and a cube root?
A square root is the number used twice to reach the value (√27 ≈ 5.196), while a cube root is the number used three times (∛27 = 3).
How do I estimate a square root by hand?
Find the nearest perfect squares on either side. For √50, that is 49 and 64, so the answer is just above 7. Averaging 50 ÷ 7 with 7 gives about 7.07, which is accurate to two decimal places.
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