NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Multiply algebraic surds

## Interactive practice questions

Consider the differences between adding like surds and multiplying like surds.

a

Find $\sqrt{3}+\sqrt{3}$3+3.

b

Find $\sqrt{3}\times\sqrt{3}$3×3.

c

Which of the following describes the difference between the expressions in part (a) and (b)?

In part (a), we are adding like surds: $\sqrt{x}+\sqrt{x}$x+x. When adding like surds, the answer always involves a surd.

In part (b), we are multiplying like surds: $\sqrt{x}\times\sqrt{x}$x×x. When multiplying like surds, the surd disappears.

A

Adding surds always results in a whole number value, whereas multiplying surds always results in a surd answer.

B

Adding surds always results in a surd answer, whereas multiplying surds always results in a whole number value.

C

In part (a), we are adding like surds: $\sqrt{x}+\sqrt{x}$x+x. When adding like surds, the answer always involves a surd.

In part (b), we are multiplying like surds: $\sqrt{x}\times\sqrt{x}$x×x. When multiplying like surds, the surd disappears.

A

Adding surds always results in a whole number value, whereas multiplying surds always results in a surd answer.

B

Adding surds always results in a surd answer, whereas multiplying surds always results in a whole number value.

C
Easy
Approx 2 minutes

Assuming $j$j is non-negative, simplify $\sqrt{j}\sqrt{j}$jj.

Assuming $u$u is non-negative, simplify $\left(\sqrt{u}\right)^2$(u)2.

Assuming $j$j and $k$k are non-negative, write the expression $\sqrt{j}\sqrt{k}$jk as a single surd.

### Outcomes

#### M8-9

Manipulate complex numbers and present them graphically

#### 91577

Apply the algebra of complex numbers in solving problems