Square root of a number

Before understanding what the square root of a number is, it is important to understand the meaning of root of a number.

Square root of a number
The root of a number is an equal factor of the number. For example, here is how to find the root of 16.

First, we need to factor 16. The different ways to factor 16 are shown below.

16 = 1 × 16

16 = 2 × 8

16 = 4 × 4

The root of 16 is 4 because 4 is the equal factor for 16. We call 4 the square root of 16 and we write √16 = 4.

4 is called square root because we have to square 4 or raise 4 to a power of 2 to get 16.

Other examples showing how to find the square root of a number.

Find the square root of 4.You can factor 4 in two different ways.

4 = 1 × 4

4 = 2 × 2

The equal factor is 2, so 2 is the square root of 4 and we write √4 = 2.

Find the square root of 64.

64 = 1 × 64

64 = 2 × 32

64 = 4 × 16

68 = 8 × 8

The equal factor is 8, so the square of 64 is 8 and we write √64 = 8.

Can the square root of a number be negative?

Yes, absolutely! If you multiply a positive number by itself, you get a positive product. If you multiply a negative number by itself, you also get a positive product.

For example, since -8 × -8 = 64, -8 is also a square root of 64. However, unless otherwise stated, the square root sign ( √ ) refers to the positive root of a number, also called principal square root.

Can the square root of a number be a real number?

For the numbers above, the square root was equal to an integer.

it is not always possible to get the square root as an integer.

Sometimes, you may get a real number when finding the square root.

For example, use the square root calculator below to find the square root of 5.

The result includes lots of numbers after the decimal point.

Ready for big time challenge? Just like long division, learn how to compute the square root without a calculator for any number that is not a perfect square.I promise you will not sweat too much!

Teachers! Do you want a ready made square roots table that students can quickly refer to as they solve their basic math problems? Get the square roots table.

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