Square Root Calculator

A square root is a number that gives the original value when multiplied by itself. For example, 5 is the square root of 25 because 5 × 5 = 25.

The square root symbol is √. When you see √n, it means you are looking for the number that can be multiplied by itself to produce n.

Follow these steps:

1. Enter the number in the input field.
2. Click the calculate button.
3. Review the square root result.
4. Check whether the number is a perfect square.
5. View the decimal or exact form if the calculator provides it.

This process is helpful when you need a quick result and do not want to estimate the answer by hand.

The basic formula is:

If x² = n, then x = √n

Here, n is the original number and x is its square root. If x multiplied by itself equals n, then x is a square root of n.

If you are learning how to find square root values manually, start by checking whether the number is a perfect square. Perfect squares have whole-number roots, such as 4, 9, 16, 25, 36, 49, and 100.

For non-perfect squares, the result is usually a decimal. You can estimate the value by finding the two perfect squares around it. For example, 10 is between 9 and 16, so √10 is between 3 and 4.

This is also the simplest way to understand how to find the square root of a number before using an online tool.

Here are a few common examples:

The square root of 100 is 10 because 10 × 10 = 100. The square root of 10 is about 3.162 because 10 is not a perfect square.

A perfect square is a number with a whole-number square root. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

If a number is not a perfect square, the answer may appear as a decimal or radical form. For example, the square root of 8 is about 2.828, but it can also be written in simplified radical form.

Sometimes you may need to simplify square root values instead of converting them fully into decimals. This is common in algebra when the answer should stay in radical form.

For example, √8 can be simplified as 2√2. If you need to simplify square root expressions, look for the largest perfect square factor inside the number. This calculator shows that simplified radical form automatically for whole numbers.

Positive numbers technically have two roots: one positive and one negative. For example, both 3 and -3 produce 9 when multiplied by themselves.

However, the square root symbol usually refers to the principal square root, which is the non-negative result. That is why √9 is normally written as 3.

Negative numbers do not have real square roots. When you enter a negative number, this calculator shows the result using the imaginary unit i.

√-9 = 3i

For most basic math, square root answers focus on real numbers, but imaginary results are shown here when the number is negative.

A square root calculator is useful when you need fast help with:

• Algebra homework
• Geometry problems
• Area and side-length calculations
• Pythagorean theorem questions
• Perfect square checks
• Scientific calculations
• Decimal square root values
• Radical expression checks

You may also find these tools useful:

• Pythagorean Theorem Calculator
• Square Calculatorcoming soon
• Cube Root Calculatorcoming soon
• Root Calculatorcoming soon
• Exponent Calculatorcoming soon
• Scientific Calculatorcoming soon
• Algebra Calculatorcoming soon

Enter your number above and use the square root calculator to get the result quickly. Review whether your answer is a perfect square, decimal, or simplified form.