Question

Identify the quadratic surd(s).

• A. $\sqrt[4]{44}$
• B. $\sqrt[4]{416}$
• C. $\sqrt[3]{3125}$
• D. $\frac{\sqrt{45}}{3}$

Answer 1

Answer: (A), (D)

$\frac{\sqrt{45}}{3}$

$\underset{–}{Concept:}$ Square root of a non-perfect square is quadratic surd.

Let's simplify each expression one by one.

$\sqrt[4]{44}=(2^2{)}^{\frac{1}{4}}=2^{\frac{1}{2}}=\sqrt{2}$

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

$\sqrt[4]{416}=(2^4{)}^{\frac{1}{4}}=2$

2 is not a quadratic surd.

$\sqrt[3]{3125}=(5^3{)}^{\frac{1}{3}}=5$

5 is not a quadratic surd.

$\frac{\sqrt{45}}{3}=\frac{\sqrt{9\times 5}}{3}=\frac{\sqrt{9}\times \sqrt{5}}{3}=\frac{3\times \sqrt{5}}{3}=\sqrt{5}$

$\sqrt{5}$ is not a quadratic surd.