Index Laws and Surds

What is are indices and surds?

This post will introduce index laws and surds, as a part of the Prelim Maths Advanced course under the topic Working with Functions and sub-part Algebraic Techniques. Indices are the plural of an index, where index represents the number of times a number is multiplied by itself. Other names may be exponent or power. For example, the index of $3^{2}$ is 2, where the base 3 is multiplied by itself 2 times, since $3^{2} = 3 \times 3 = 9$ . Surds are the irrational root of an integer, where it can’t be simplified to remove the root. For example, $\sqrt{3}$ , however $\sqrt{9}$ is not a surd, as it can be simplified into $3$ .

Index laws

The following two videos cover your index laws. The first video covers the multiplication, division, powers of indices, and the respective outcome of each of them, whilst the second video covers negative and fractional indices.