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CanadaON
Grade 11

Multiply algebraic radicals

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 radical.

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

A

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

B

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

C
Easy
1min

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

Easy
< 1min

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

Easy
< 1min

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

Easy
< 1min
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Outcomes

11U.A.3.2

Verify, through investigation with and without technology, that sqrt(ab)=sqrt(a) x sqrt(b), a>=0, b>=0, and use this relationship to simplify radicals

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