# 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?

1²   =   1  x  1   =   1

Therefore ## Square root of 4

Which figure squared (multiplied by itself) gives 4?

2²   =   2  x  2   =   4

So ## Square root of 9

What figure squared (times by itself) gives 9?

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