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RRB Non Technical Model Papers 10 with solutions

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Question : 7 of 100

Marks: +1, -0

The smallest among,

6\sqrt{12},3\sqrt{4},4\sqrt{5},\sqrt{3}

is

$6\sqrt{12}$
$3\sqrt{4}$
$\sqrt{3}$
$4\sqrt{5}$

Solution:

Concept:

To compare surds with different indices, convert them to the same radical index.

Explanation:

The indices are

6,3,4,2

.

LCM of indices

=12

.

\sqrt[6]{12}=12^{1/6}=12^{2/12}=\sqrt[12]{144}

\sqrt[3]{4}=4^{1/3}=4^{4/12}=\sqrt[12]{256}

\sqrt[4]{5}=5^{1/4}=5^{3/12}=\sqrt[12]{125}

\sqrt{3}=3^{1/2}=3^{6/12}=\sqrt[12]{729}

Comparing radicands:

125<144<256<729

.

So the smallest surd is

\sqrt[12]{125}=\sqrt[4]{5}

.

Answer:

The smallest is

\sqrt[4]{5}

, i.e. option D.

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