# Surds and Indices

Surd:

A number that can't be simplified to remove a square root (or cube root etc).

Indices:

The index of a number shows you how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64.

The plural of index is indices. (Another name for index is exponent or power)

1

(17)3.5 x (17)? = 178

2

If $${\Bigg({a \over b}\Bigg)}^{x-1}=\Bigg({b \over a}\Bigg)^{x-3}$$, then the value of x is:

3

Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:

4

If 5a = 3125, then the value of 5(a - 3) is:

5

If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to: