Question

Express a to the power 1/3 √ab^3 to pure surd

Answer 1

Both of the following are pure surds as long as a and b are rational number and root is a integer!
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Answer 2

Answer:

Given : $a^\frac{1}{3}$ and $\sqrt{ab^3}$

To express : The given form in pure surd

Solution : The pure surd form is  $\sqrt[n]{x}$ or we can say  a surd having no rational factor except unity.

1) $a^\frac{1}{3}$

We can re-write this form in $\sqrt[3]{a}$

This form is in pure surd.

2)  $\sqrt{ab^3}$ this is in the form of pure surd

Pure surd form is $\sqrt[n]{a^nx}$ also.

where n=1 a=x and b=a