# Indices & Roots

## Indices - Introduction

Indices, exponents or powers are numbers that tell us how often a number is to be multiplied by itself in a mathematical expression.
A power is usually represented by a raised smaller number on the right side of the number that it belongs
to (eg: 3²). The example on the right shows the function of a power more clearly. If the power is 3, the
number (in this case five), is multiplied together 3 times. If the power is to, it is multiplied together twice
and so on. Exponents (powers) can not only be a simple number. They can also be negative and
fractional and this is where it becomes a bit more complicated.
Powers in Words
Here are a few ways to say different power.
•
2² - “Two squared”, “Two to the second power two” & “Two to the power of two”.
•
6³ - “Six cubed”, “Six to the third power” & “Six to the power of three.”
If the power is larger than 4, there is no short expression such as squared or cubed, so you have to use
“to the power of” or “to the ... power”.
Roots - Introduction
Square rooting a number is basically the opposite of squaring it. The root sign is represented by a tick with a number that represents the type of root
(the power it belongs to) and a line at the end which is above the number that is suppose to be rooted
(shown in the example on the right). In the example, we see that 5² or 5x5 is equal to 25. Now if we
square root 25, we get 5 again. So it is basically just the reverse of squaring. We cannot just square root,
but also calculate the 3rd root, 4th root and so on. Underneath are a few example of other square roots
signs. The small number above the tick represents the type of root.
There is no simple mathematical way to calculate square roots without a calculator. This is why we usually tend to use on for rooting numbers.
However, you should try and learn the square numbers and their roots between 1 and 100. This will not only be helpful in certain situations, but it will
also help you remember the concept of powers and roots.
More on Indices and Roots
If you understand what indices are, you should move on to some more detailed explanations and the laws of indices. If you are already familiar with
indices and would like to work on a more advanced topic, you can also jump straight ahead to negative and fractional indices. You can also attempt to
do some surds which involve roots. Please share this page if you like it or found it helpful!
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Chapter 7.0: Learning Outcomes
Students will be introduced to the concept of indices!
Students will be familiarised with the concept of roots!

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