Square Root Calculator

What is a Square Root?

The square root of a number x is a value y such that \(y^2 = x\). For example, \(\sqrt{144} = 12\) because \(12 \times 12 = 144\).

Perfect squares from 1 to 20

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400. Knowing these by sight makes estimating other square roots much easier, because you can see which two perfect squares your number falls between.

How to use this calculator

1. Enter the number you want the root of, such as 49.
2. If needed, choose a root index, like 2 for a square root or 3 for a cube root.
3. Read the decimal result, and check whether the number is a perfect square or another perfect power.
4. Use the step-by-step explanation to see how the answer was found.

The formula explained

The formula \(root[n]{x} = x^{1/n}\) means the n-th root of a number is the value that, raised to the n-th power, gives back x. For square roots, n = 2, so \(\sqrt{x} = x^{1/2}\).

• x = the number you want to find the root of
• n = the root index, such as 2 for a square root or 3 for a cube root

Step by step method

1. Rewrite the problem as finding a number that, when multiplied by itself, equals the original number.
2. Check whether the number is a perfect square, like 49 = 7^2, so the square root is exact.
3. If it is not a perfect square, estimate the answer using nearby squares or use the calculator for a decimal result.

Worked example

Problem. Find the square root of 49.

1. Look for a number that squared gives 49.
2. Since 7^2 = 49, the number is 7.
3. So the square root of 49 is 7.

Tips and common mistakes

• If the number is negative, a real square root does not exist, because no real number squared is negative.
• For square roots, always remember that \(\sqrt{x}\) usually means the principal, nonnegative root.

Frequently asked questions