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The greatest onr of the \( \Large \sqrt{2},\sqrt[3]{3},\sqrt[6]{6},\sqrt[5]{5} \) is:

A) \( \Large \sqrt{2} \)
B) \( \Large \sqrt[3]{3} \)
C) \( \Large \sqrt[6]{6} \)
D) \( \Large \sqrt[5]{5} \)

Correct Answer:


B) \( \Large \sqrt[3]{3} \)

Description for Correct answer:
\( \Large \sqrt{2} \rightarrow 2^{ \frac{1}{2}} \rightarrow 2^{\frac{15}{30}} = \sqrt[30]{2^{15}} = \sqrt[30]{32768}\)

\( \Large \sqrt[3]{3} \rightarrow 3^{\frac{1}{3}} \rightarrow 3^{\frac{10}{30}}= \sqrt[30]{3^{10}} = \sqrt[30]{59049}\)

\( \Large 6\sqrt{6} \rightarrow 6^{\frac{1}{6}} \rightarrow 6^{\frac{5}{30}} = \sqrt[30]{6^{5}} = \sqrt[30]{7776}\)

\( \Large \sqrt[5]{5} \rightarrow 5^{\frac{1}{5}} \rightarrow 5^{\frac{6}{30}} = \sqrt[30]{5^{6}} = \sqrt[30]{15625} \) is the greatest.

Part of solved Indices and Surd questions and answers : >> Elementary Mathematics >> Indices and Surd

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Similar Questions

1). Given \( \Large \sqrt{2} =1.414\).The valueof \( \Large \sqrt{8} +2\sqrt{32}-3\sqrt{128}+4\sqrt{50}\) is:

A). 8.484

B). 8.526

C). 8.426

D). 8.876

2). If \( \Large \sqrt{15} =3.88\),then what is the value of \( \Large \sqrt{\frac{5}{3}} \).

A). 1.29333....

B). 1.2934

C). 1.29

D). 1.295

3). The ratinalising factor of \( \Large 3\sqrt{3} \) is:

A). \( \Large \frac{1}{3}\)

B). 3

C). -3

D). \( \Large \sqrt{3} \)

4). \( \Large \sqrt{2+\sqrt{2+\sqrt{2+...}}} \) is equal to:

A). \( \Large \sqrt{2} \)

B). \( \Large 2\sqrt{2}\)

C). 2

D). 3

5). The value of\( \Large 2+\sqrt{0.09}-\sqrt[3]{0.008}-7%\) of 2.80 is:

A). 0

B). 0.01

C). -1

D). 0.001

6). The value of \( \Large \left(\sqrt[3]{3.5}+\sqrt[3]{2.5}\right) \{ \left(\sqrt[3]{3.5}\right)^{2}-\sqrt[3]{8.75} + \left(\sqrt[3]{2.5}\right)^{2} \} \) is:

A). 5.375

B). 1

C). 6

D). 5

7). The value of \( \Large \left(3+2\sqrt{2}\right)^{-3}+ \left(3-2\sqrt{2}\right)^{-3} \) is:

A). 189

B). 180

C). 108

D). 198

8). \( \Large \frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}}-\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}}+\frac{2\sqrt{2}}{\sqrt{5}+\sqrt{3}} \) is equal to:

A). 0

B). \( \Large 2\sqrt{15} \)

C). \( \Large 2\sqrt{10} \)

D). \( \Large 2\sqrt{6} \)

9). The value of \( \Large \frac{1}{\sqrt{3.25}+\sqrt{2.25}}+\frac{1}{\sqrt{4.25}+\sqrt{3.25}}+\frac{1}{\sqrt{5.25}

+\sqrt{4.25}}+\frac{1}{\sqrt{6.25}+\sqrt{5.25} }\) is:

A). 1

B). 1.25

C). 1.5

D). 2.25

10). \( \Large \frac{3^{0}+3^{-1}}{3^{-1}-3^{0}} \) is simplified to:

A). -2

B). -1

C). 1

D). 2