Question

8. By what smallest number should 10584 be multiplied so that the product may be a perfect square?
9. What should be the least number by which when 23808 be divided, the quotient may be a perfect square
10. (i) Find the square root of 11025 by prime factorisation​

Answer 1

Prime factorisation of 10584 is  

10584=2  

3×3  

2 ×72

 

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 ×72

 

The square root of this new number is

24 ×3  4 ×72

 =2  

2 ×3  2

×7

=4×9×7

=63×4

=192