About the Square Root Calculator
The square root of a number is the value that gives the number when multiplied by itself, so the square root of 144 is 12. This calculator finds square roots, cube roots and the 4th, 5th and 10th roots of any number. For whole numbers it also writes the answer in simplified radical form, so the square root of 72 appears as 6√2, and it tells you whether the number is a perfect square, cube or power. Negative numbers work with odd roots such as the cube root; even roots of negative numbers are not real and give a clear message.
Updated October 2026
How to use the Square Root Calculator
- 1Type the number you want the root of.
- 2Choose square root, cube root or a higher root.
- 3Read the decimal answer in the highlighted box.
- 4Check the simplified radical and the perfect-power row underneath.
- 5Press Copy result to copy the answer.
Squares and roots
Squaring and taking a square root are opposite operations. If a square has an area of 49 square metres, each side is the square root of 49, which is 7 metres. Roots appear in geometry, in the Pythagorean theorem, in the quadratic formula and in statistics, where the standard deviation is the square root of the variance.
Perfect squares worth knowing
- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
- 121, 144, 169, 196, 225
- Perfect cubes: 1, 8, 27, 64, 125, 216
- Every perfect square ends in 0, 1, 4, 5, 6 or 9
- Square roots of non-perfect squares are irrational
How simplification works
The tool divides your whole number by the largest perfect power it contains. For 72 and a square root, the largest square factor is 36, leaving 2 under the root and 6 outside. For 54 and a cube root, the largest cube factor is 27, giving 3∛2. When the inside is 1, the number was a perfect power and the answer is a whole number.
Related tools
The Pythagorean Theorem Calculator uses square roots to find the missing side of a right triangle, the Quadratic Equation Solver needs them for the discriminant, and the Exponent Calculator covers powers. The Log Calculator and the Standard Deviation Calculator are good next steps.
Features
- Square root, cube root, 4th, 5th and 10th roots
- Simplified radical form for whole numbers
- Perfect square, cube and power check
- Cube roots of negative numbers
- Answers to about 14 significant digits
- Shows the square of the number as well
- Runs in your browser
Frequently asked questions
How do I find a square root without a calculator?
Start with the nearest perfect squares. The square root of 50 sits between 7 (49) and 8 (64), very close to 7. Refine by guessing, dividing 50 by the guess and averaging the two: (7 + 50÷7) ÷ 2 ≈ 7.07. Repeating this gets you to many digits quickly.
What does simplified radical form mean?
It means pulling out any perfect square factors from under the root sign. Since 72 = 36 × 2 and the square root of 36 is 6, the square root of 72 is written 6√2. Teachers often want answers in this exact form instead of 8.485.
What is a perfect square?
A perfect square is a whole number whose square root is also a whole number, such as 1, 4, 9, 16, 25 and 144. The calculator tells you whether your number is one, and does the same for perfect cubes and higher powers.
Can you take the square root of a negative number?
Not within real numbers, because no real number multiplied by itself is negative. The answer is an imaginary number, such as 2i for the square root of −4. This calculator shows a message for even roots of negative numbers. Odd roots, such as the cube root of −27, which is −3, work normally.
What is a cube root?
A cube root is the number that, multiplied by itself twice more, gives the original. The cube root of 27 is 3 because 3 × 3 × 3 = 27. Select cube root in the root menu to find it, including for negative numbers.
Is the square root of 2 a fraction?
No. The square root of 2 is irrational, meaning its decimal form (1.41421356…) never ends or repeats and it cannot be written as a fraction of whole numbers. The calculator shows it to about 14 significant digits, which is enough for almost any use.