Question

State which of the following are pure surds and mixed surds:

$\frac{3}{4}\sqrt{8}$

• A. Pure surd
• B. Mixed surd
• C. Not a surd
• D. None of above

Answer 1

Answer: (B)

Mixed surd

$\frac{3}{4}\sqrt{8}$

$=\frac{3}{4}\sqrt{2\times 2\times 2}$

$=\frac{3}{4}\times 2\sqrt{2}$

$=\frac{3}{2}\sqrt{2}$

A surd having a rational co-efficient other than unity is called a mixed surd.
In other words if some part of the quantity under the radical sign is taken out of it, then it makes the mixed surd

Thus, $\frac{3}{4}\sqrt{8}$ is a mixed surd as $\frac{3}{4}$ is outside the radical sign and $\sqrt{8}$ is a surd