The square root calculator on this page answers a simple question very quickly: which number, multiplied by itself, gives the number you entered? If you type 144, the answer is 12, because 12 multiplied by 12 equals 144. Students meet square roots in school mathematics, in algebra and in geometry, and adults meet them again when they work out areas, distances, sizes and measurements. This free tool removes the guesswork, so you can check homework, verify a measurement or finish a calculation without reaching for a scientific calculator.

It is useful for school and college students, for teachers preparing examples, for parents helping with homework, and for anyone working with areas and lengths. Builders, designers, gardeners and DIY enthusiasts often need a square root when a square area is known and a side length is needed. If a square room, garden bed or tile layout covers 144 square feet, each side is 12 feet long. The same idea applies to circles, triangles and right-angled triangles, where Pythagoras’ theorem often ends with a square root. Because the result is shown to several decimal places, the tool is also handy for science, engineering and everyday estimation.

How to Use the Square Root Calculator

1. Enter your number. Type any zero or positive number into the box above. Decimals are accepted, so 2.5 and 0.25 both work.
2. Press Calculate Square Root. The tool works out the square root at once, with no page reload.
3. Read the result. You will see the full square root, the value rounded to two decimal places, whether the number is a perfect square, and its cube root.
4. Check the answer. The check line multiplies the result by itself, so you can see that it returns to your original number.
5. Try another number. Clear the box and repeat the steps as often as you need.

Worked Example: The Square Root of 144

Suppose you need the side length of a square garden that covers 144 square metres. Enter 144 into the calculator and press Calculate Square Root. The tool returns 12, because 12 multiplied by 12 equals 144. The rounded result is also 12.00, and the perfect square answer is Yes, which confirms that 144 is a perfect square. The cube root shown alongside is 5.2415, which is a useful extra check when you are working in three dimensions.

Now try a number that is not a perfect square. The square root of 2 is 1.414214, which rounds to 1.41. Multiply 1.414214 by itself and you return to 2.000000, allowing for rounding. This is why the calculator shows several decimal places: a rounded answer such as 1.41 is fine for a quick estimate, but the longer value is better when the result feeds into another calculation. Always keep extra decimal places until the final step, and round only at the end.

Understanding Square Roots

A square root undoes squaring. Squaring 9 gives 81, so the square root of 81 is 9. Every positive number has two square roots, one positive and one negative, because negative 9 multiplied by negative 9 also gives 81. By convention, the square root symbol means the positive root, and that is the value this calculator returns. Zero is a special case: the square root of zero is zero. Negative numbers have no real square root, which is why the calculator asks for zero or a positive number.

Perfect squares are the numbers you get by squaring whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144. Learning the first few perfect squares makes estimation much faster. If a number sits between 100 and 121, its square root sits between 10 and 11. If it sits between 144 and 169, its square root sits between 12 and 13. That habit helps you spot an answer that cannot be right, even before you check it with a calculator.

Tips for Accurate Results

• Enter the exact number you were given. A small typing error, such as 114 instead of 144, changes the answer completely.
• For areas, check your units first. Square feet give a side length in feet, and square metres give a side length in metres.
• Keep full precision during a multi-step calculation and round only the final answer.
• Use the perfect square check as a sanity test. If you expected a whole number and the tool says No, re-check the original number.
• Remember that the square root of a number smaller than 1 is larger than the number itself. For example, the square root of 0.25 is 0.5.

Frequently Asked Questions

What is the square root of 144?

The square root of 144 is 12, because 12 multiplied by 12 equals 144. It is a perfect square, and it is one of the most common square roots used in school mathematics.

What is the square root of 2?

The square root of 2 is approximately 1.414214. It is an irrational number, which means its decimal places go on for ever without repeating, so any calculator answer is rounded.

Can a square root be negative?

A positive number has both a positive and a negative square root. The square root of 25 is 5 and negative 5. The square root symbol on its own normally means the positive value, which is what this calculator shows.

What is the square root of a negative number?

A negative number has no real square root, because no real number multiplied by itself gives a negative result. In advanced mathematics, imaginary numbers are used instead, but this calculator is designed for real, everyday calculations.

How do I find a square root without a calculator?

Estimate between two perfect squares, then refine your guess. For 50, the answer sits between 7 and 8, because 49 and 64 are perfect squares. Try 7.1, square it, and adjust up or down until you reach the accuracy you need.

Use this square root calculator whenever you need a fast, checked answer. Bookmark the page for homework, revision and everyday measurement work.