# Square root problems

*In this lesson, you'll learn how to solve square root problems.** Remember **√ is the symbol for square root.*

## So what is the square root of a number n (√n)?

It's that figure which squared (i.e. multiplied by itself) gives n.

If n is a square number (perfect square) (1, 4, 9, 16, 25, 36, 49, 64, 81, 100 etc), its square root is a whole number.

However, if n is a non-square number (2, 3, 5, 6, 7, 8, 10, 11, 12, 13 etc), its square root is a decimal and your calculator will prove useful!

*Let's take a look at the square roots of square numbers first.*

## How to find square root of 1

*What figure squared (times by itself) gives 1?*

The answer is 1 because

**1² = 1 x 1 = 1**

Therefore

Square root of 4

*Which figure squared (multiplied by itself) gives 4?*

The answer's 2

**2² = 2 x 2 = 4**

So

Square root of 9

*What figure squared (times by itself) gives 9?*

The answer's 3

**3² = 3 x 3 = 9**

So

Now try finding the square roots of the remaining square numbers up to 100

Here are the workings out!

- √16 = 4 (4² = 4 x 4 = 16)
- √25 = 5 (5² = 5 x 5 = 25)
- √36 = 6 (6² = 6 x 6 = 36)
- √49 = 7 (7² = 7 x 7 = 49)
- √64 = 8 (8² = 8 x 8 = 64)
- √81 = 9 (9² = 9 x 9 = 81)
- √100 = 10 (10² = 10 x 10 = 100)

*See how these square roots are whole numbers?*

## Next how about the square roots of non-square numbers?

Reach for your calculator, enter 2 followed by the square root (√) button

The display should show

**1.414213562**

You've just worked out √2 - the square root of 2.

*Notice how it's a decimal and this applies to the square roots of other non-square numbers - for instance, check the following on your calculator*

- √3 = 1.732050808
- √5 = 2.236067978

- √6 = 2.449489743

- √7 = 2.645751311

- √8 = 2.828427125
- √10 = 3.16227766

- √11 = 3.31662479

- √12 = 3.464101615

- √13 = 3.605551275

## Happy you can now handle square root problems?

As you can see, finding the square root of a number n may or may not require use of your calculator depending on whether n is a square number (square root = whole number) or a non-square number (square root = decimal).

For related topics click:

Square numbers

Cube numbers

Cube roots

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