Surds

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

Multiply algebraic surds

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

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