Question

How many of the given following are surds ?

(i) $\sqrt[3]{37}$ (ii) $\sqrt[4]{40.16}$ (iii) $\sqrt[3]{3\sqrt{8}}$
(iv) $\sqrt{-5}$ (v) $\frac{1}{\sqrt{0.16}}$ (vi) $\sqrt{0.333}$
(vii) $\sqrt{576}$ (viii) $\sqrt{\frac{5}{4}}$ (ix) $\sqrt{\frac{22}{7}}$
(x) $\sqrt[3]{32\sqrt{9}}$.

• A. 6
• B. 7
• C. 8
• D. 9

Answer 1

Answer: (B)

7

(i)$\sqrt[3]{37}$ cannot simplified to remove root.
(ii) $\sqrt[4]{40.16}=\sqrt[4]{4(.4{)}^2}=\sqrt{.4}$ cannot simplified to remove root.

(iii) $\sqrt[3]{3\sqrt{8}}=\sqrt[3]{3\sqrt{(2{)}^3}}=\sqrt{2}$ cannot simplified to remove root.
(iv) $\sqrt{-5}=\sqrt{5}i$ is a complex number.
(v) $\frac{1}{\sqrt{0.16}}=\sqrt{\frac{100}{16}}=\frac{10}{4}=2.5$ is not a surd, as it is rational.

(vi) $\sqrt{0.333}$ cannot simplified to remove root.
(vii) $\sqrt{576}=24$, which is not a surd, as it is rational.

(viii) $\sqrt{\frac{5}{4}}$ $=\frac{\sqrt{5}}{2}$cannot simplified to remove root.

(ix) $\sqrt{\frac{22}{7}}$ cannot simplified to remove root.

(x) $\sqrt[3]{32\sqrt{9}}$ $\sqrt[3]{32\times 3}$ cannot simplified to remove root.
Hence, $3$ numbers are not surds. Remaining $7$ numbers are surds.

Therefore, option $C$ is correct.