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Find the smallest number by which $9408$ must be divided so that the quotient is a perfect square.

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Smaller number:

5

, Quotient:

3036

, Square root:

54

Smaller number:

3

, Quotient:

3136

, Square root:

56 .

Smaller number:

7,

Quotient:

3236

, Square root:

57 .

Data insufficient

answer is B.

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Detailed Solution

Given number is 9408
We have 9408=

2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 7 \times 7

If we divide 9408 by the factor 3 then

9408 \div 3 = 3136

\Rightarrow 9408 \div 3 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7

But,

\sqrt{3136} = 2 \times 2 \times 2 \times 7

\Rightarrow \sqrt{3136} = 56

Therefore, option (2) is correct.

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Find the smallest number by which 9408 must be divided so that the quotient is a perfect square.

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Find the smallest number by which $9408$ must be divided so that the quotient is a perfect square.