by what smallest number should 10584 be multiplied so that product may be a perfect square ? also find the square root of the new number.
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Answer:
Prime factorisation of 10584 is
10584=2
3
×3
2
×7
2
Now for the above to be a perfect square we can see that we need to multiply 2×3=6
∴ the least number to be multiplied to 10584 to make it a perfect square is 6
∴10584×6=2
3
×3
3
×7
2
×2×3=2
4
×3
4
×7
2
The square root of this new number is
2
4
×3
4
×7
2
=2
2
×3
2
×7
=4×9×7
=63×4
=192
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