Interactive practice questions
Consider the differences between adding like surds and multiplying like surds.
Find $\sqrt{3}+\sqrt{3}$√3+√3.
Find $\sqrt{3}\times\sqrt{3}$√3×√3.
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.
Adding surds always results in a whole number value, whereas multiplying surds always results in a radical answer.
Adding surds always results in a radical answer, whereas multiplying surds always results in a whole number value.
Assuming $j$j is non-negative, simplify $\sqrt{j}\sqrt{j}$√j√j.
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 $\sqrt{j}\sqrt{k}$√j√k as a single radical.