Question

Identify whether the resulting expression is a quadratic surd or not.

$\frac{\sqrt[3]{38}}{\sqrt[8]{816}}$

• A. Yes.
• B. No.
• C. Cannot be determined.

Answer 1

The correct option is A Yes.

Let's simplify $\frac{\sqrt[3]{38}}{\sqrt[8]{816}}$ by expanding each term.

$\frac{\sqrt[3]{38}}{\sqrt[8]{816}}=\frac{(2\times 2\times 2{)}^{\frac{1}{3}}}{\sqrt[8]{816}}=\frac{2}{(2\times 2\times 2\times 2{)}^{\frac{1}{8}}}=\frac{2^{\frac{1}{2}\times 2}}{2^{\frac{4}{8}}}=\frac{(\sqrt{2}{)}^2}{2^{\frac{1}{2}}}$
$=\frac{\sqrt{2}\times \sqrt{2}}{\sqrt{2}}$
(canceling $\sqrt{2}$ from numerator and denominator)
$=\sqrt{2}$

$\sqrt{2}$ is a quadratic surd.