Question

By what smallest number should 10584 be multiplied ao that product is perfect square

Answer 1

hi there !
Here's the answer:

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¶¶¶ Steps:

• Resolve into prime factors.
• Express the No. as product of prime factors in exponential form.
• Now, the prime factors which are not having 2 as their powers should be multiplied on both sides to get a perfect square.



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Now,

2 | 10584
2 | 5292
2 | 2646
… | 1323

(1323 is a Prime Number)

10584 = 2² × 2 × 1323

The prime factors 2 & 1323 aren't having 2 as their power.

•°• The 10584 should be multiplied by (2×1323)= 2646 to make it a perfect square.

•°• Required No. (No. to be Multiplied) = 2646
& the perfect square is 10584× 2646 = 28005264.


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:)

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Hope it helps