Numbers 1-12 squared

## Square numbers

A **square number** is a number multiplied by itself. The symbol is ^{2} (we call it **exponent**). The number squared is called the **base**:

We can read this as two/three/four to the second power.

A **cube number** is a number multiplied by itself 3 times:

Square roots

## Square roots

The root of a number y is another number, which when multiplied by itself a given number of times, equals y. The second root (also called the **square root**) of 16 is 4:

For every even-degree root (2nd, 4th, 6th ....) there are two roots. This is because multiplying two positive or two negative numbers both produce a positive result. E.g:

Thus, $√^2{16}=±4$

The value inside the symbol √(called **radical**) is called **radicand**.
For $√^3{27}$ 27 is radicand and 3 is the **index**.

Exponents 0, 1 and higher

## Exponents

The exponent of a number x says how many times to multiply the number x by itself. Number x is called the **base**.

There are some special exponents we need to remember:

Exponents and roots with fractional base

Simplify square root

## Simplifying square roots

To simplify roots you can use Product Property of Square Roots:

At first, find the perfect square inside the square root:

This can be written as 2√6

Numerical expressions with exponents

Numerical expressions with roots and exponents

## Simplifying square roots

To simplify roots you can use Product Property of Square Roots:

At first, find the perfect square inside the square root:

This can be written as 2√6

You can also use these formulae: