Question

State which kind of surd is $5\sqrt[3]{3135}$

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

Answer 1

The correct option is B Mixed surd

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. For example, each of the surds $2\sqrt{7},3\sqrt{6}$

$5\sqrt[3]{3135}=\sqrt[3]{3125\times 27\times 5}=\sqrt[3]{3(5{)}^3\times (3{)}^3\times 5}$

It is a mixed surd.