Sauqre Root Calculator

Calculate square roots accurately with our online square root calculator. Learn the formula, see examples, and understand how to interpret results.

What is a Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 × 5 = 25. Square roots are important in many areas of mathematics, including geometry, algebra, and calculus.

Square Root Formula

For a non-negative real number a, the square root is denoted as √a and satisfies the equation:

√a × √a = a

Square roots can be calculated for both perfect squares (numbers like 16, 25, 36) and non-perfect squares (numbers like 2, 3, 5). For non-perfect squares, the result is an irrational number that cannot be expressed as a simple fraction.

How to Calculate Square Roots

There are several methods to calculate square roots:

Prime Factorization Method

1. Factorize the number into its prime factors.

2. Group the prime factors into pairs.

3. Multiply one factor from each pair to get the square root.

Long Division Method

1. Separate the number into pairs of digits from the decimal point.

2. Find the largest number whose square is less than or equal to the first pair.

3. Subtract and bring down the next pair.

4. Double the quotient and find a digit to place after it.

5. Repeat until desired accuracy is achieved.

Using a Calculator

Our square root calculator uses a combination of these methods to provide accurate results quickly.

Note

Square roots of negative numbers are not real numbers. They are complex numbers, which are beyond the scope of this calculator.

Examples of Square Roots

Here are some examples of square roots:

Number	Square Root	Verification
16	4	4 × 4 = 16
25	5	5 × 5 = 25
36	6	6 × 6 = 36
2	≈1.4142	1.4142 × 1.4142 ≈ 2
3	≈1.7321	1.7321 × 1.7321 ≈ 3

As you can see, perfect squares have exact integer square roots, while non-perfect squares have approximate decimal square roots.

FAQ

What is the square root of 0?: The square root of 0 is 0, because 0 × 0 = 0.
Can I calculate the square root of a negative number?: No, the square root of a negative number is not a real number. It is a complex number, which involves the imaginary unit i.
How do I calculate the square root of a fraction?: The square root of a fraction a/b is √a/√b. You can calculate the square roots of the numerator and denominator separately.
What is the difference between a square root and a square?: A square is a number multiplied by itself (e.g., 5 × 5 = 25). A square root is a number that, when multiplied by itself, gives the original number (e.g., √25 = 5).