Question

6. Find the smallest number by which 9408 must be divided so that it becomes a perfect square.

Answer 1

9408=2×2×2×2×2×2×3×7×79408=2×2×2×2×2×2×3×7×7

The Prime factor 2 and 7 occurs in pairs.

But prime factors 3 doesn't have a pair.
3 is the smallest number by which 9408 must be divided so that it become a perfect square.
Perfect square =9408×3=3136=9408×3=3136=2×2×2×2×2×3×7×7=2×2×2×2×2×3×7×7
The prime factors 2 and 7 occurs in pairs.
But Prime factors 3 doesn't have a pair.
33 is the smallest number by which 9408 must be divided so that it becomes a perfect square.
Perfect square =9408×3=3136=9408×3=3136=2×2×2×2×2×2×7×7=2×2×2×2×2×2×7×7
Square root =2×2×2×7=56=2×2×2×7=56

Answer :56

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Answer 2

2  9408            √ 9408=2×2×2×2×2×2×7×7×3
2  4704                        =2²×2²×2²×7²×3
2  2352              ∴9408 is not a perfect square number to make it a perfect 
2  1176                 square number we need to divide 9408 by 3
2  588
2  294                                    9408÷3=3136
7  147
7  21
3  3
    1