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The greatest among the numbers \( \Large \sqrt[4]{2}, \sqrt[5]{3}, \sqrt[10]{6} \ and \ \sqrt[20]{15} \) is

A) \( \Large \sqrt[20]{15} \)
B) \( \Large \sqrt[4]{2} \)
C) \( \Large \sqrt[5]{3} \)
D) \( \Large \sqrt[10]{6} \)

Correct Answer:



C) \( \Large \sqrt[5]{3} \)

Description for Correct answer:

LCM of 4, 5, 10 and 20 = 20

\( \Large \sqrt[4]{2} = \left(2\right)^{\frac{1}{4}} = \left(2^{5}\right)^{\frac{1}{20}} = \left(32\right)^{\frac{1}{20}} \)

\( \Large \sqrt[5]{3} = \left(3\right)^{\frac{1}{5}} = \left(3^{4}\right)^{\frac{1}{20}} = \left(81\right)^{\frac{1}{20}} \)

\( \Large \sqrt[10]{6} = \left(6\right)^{\frac{1}{10}} = \left(6^{2}\right)^{\frac{1}{20}} = \left(36\right)^{\frac{1}{2}} \)

\( \Large \sqrt[20]{15} = \left(15\right)^{\frac{1}{20}} \)

The greatest number is \( \Large \left(81\right)^{\frac{1}{20}} i.e. \sqrt[5]{3} \)

Part of solved Simple and Decimal fraction questions and answers : >> Elementary Mathematics >> Simple and Decimal fraction

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Similar Questions

1). If the fraction \( \Large \frac{a}{b} \) is positive, then which of the following must be true?

A). a > 0

B). b > 0

C). ab > 0

D). a + b > 0

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A). \( \Large \frac{730}{77} \)

B). \( \Large \frac{73}{77}\)

C). \( \Large \frac{73}{770}\)

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3). If 0.764y = 1.236x, then what is the value of \( \Large \frac{y - x}{y + x} \)?

A). 0.764

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4). Find the HCF of \( \Large \frac{5}{6} \),\( \Large \frac{5}{18} \) and \( \Large \frac{25}{32} \)

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D). Cannot be determined

5). The pair of rational numbers that lies between \( \Large \frac{1}{4} \ and \ \frac{3}{4} \) is

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6). How many pieces of 13.2 cm can be cut from a 330 cm long rod?

A). 25

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10). \( \Large \frac{0.04}{0.03} \ of \ \frac{ \left( 3\frac{1}{3} - 2\frac{1}{2}\right) \div \frac{1}{2} \ of \ 1\frac{1}{4} }{\frac{1}{3} + \frac{1}{5} \ of \ \frac{1}{9} } \)

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