Question

root
8. By what smallest number should I0584 be multiplied so that the product may be a perfect square.

tell me it's right answer.​

Answer 1

Step-by-step explanation:

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