Square Root Calculator
Find the square root of any number to high precision, spot perfect squares instantly, and switch to cube roots — with a check on every answer.
Result
How It Works
The square root of a number is the value that, multiplied by itself, gives that number back: the square root of 144 is 12 because 12 × 12 = 144. Numbers whose square root is a whole number are called perfect squares — 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144 are the first twelve. Most numbers are not perfect squares, so their roots are long decimals: the square root of 2 is 1.4142… and never ends or repeats.
The cube root works the same way with three multiplications: the cube root of 125 is 5 because 5 × 5 × 5 = 125. Every answer on this page comes with a check line that multiplies the result back out, so you can see the root is right.
Worked examples: √144 = 12 (12 × 12 = 144 — a perfect square). √2 ≈ 1.4142 (1.4142 × 1.4142 ≈ 2). Cube root of 125 = 5 (5 × 5 × 5 = 125 — a perfect cube).
How to Use This Calculator
Enter a number, pick square or cube root, and the answer updates live with a check line underneath.
- Enter your number — any positive number works for square roots; cube roots also accept negatives.
- Pick the root type — square root (√x) or cube root (∛x) from the dropdown.
- Read the result — the calculator tells you whether the number is a perfect square or cube, and shows the multiplication that proves the answer.
The Reset button restores the example (√144) so you can start over.
Tips and Practical Advice
Square roots come up in geometry, statistics, construction and everyday estimation — and a rough feel for them makes the exact answer easier to trust.
- Estimate before you calculate. √50 sits between √49 = 7 and √64 = 8, so the answer must be just above 7 — and indeed it is 7.0711.
- Learn the perfect squares to 15². Knowing 12² = 144, 13² = 169 and 15² = 225 by heart makes mental estimates fast and catches typos.
- Use roots for areas and sides. A square room of 25 m² has sides of √25 = 5 m — the square root turns an area back into a length.
- Do not round too early. If a root feeds into another calculation, keep the full decimal and round only the final answer, or small errors grow.
Frequently Asked Questions
What is the square root of 144?
12, because 12 × 12 = 144. Since 144 has a whole-number root, it is a perfect square.
What is the square root of 2?
Approximately 1.4142. It is an irrational number — its decimal never ends and never repeats — so any decimal answer is an approximation.
Can you take the square root of a negative number?
Not in real numbers: no real number multiplied by itself gives a negative. The cube root of a negative number is fine, though — the cube root of −8 is −2.
What is a perfect square?
A number that is the square of a whole number, like 144 = 12². Its square root is exact, with no decimal tail.
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