Year 10 Interactive Maths - Second Edition

Multiplication of Surds

Multiplication of Entire Surds

In general:

The multiplication of like surds gives a rational number. That is:

Example 11

Solution:

Short way:

Short way:

In general:

The multiplication of unlike surds gives an irrational number.

Example 12

Solution:

Note:

Always give your answer in the simplest possible form.

Multiplication of Mixed Surds

We can get the same result by multiplying the radicands and multiplying the coefficients, as follows:

In general:

Example 13

Solution:

Alternatively: