1.

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.(i) 525                  (ii) 1750                      (iii) 252               (iv) 1825(v) 6412

Answer» (i) `23^2 > 525 > 22^2`
to make it square , add `= 23^2 - 525`
`= 529 - 525 = 4`
new number =`525 +4 = 529`
`sqrt529 = 23`
(ii) `80^2 < 6412 < 81^2`
add `81^2 - 6412`
`= 6561 - 6412`
`= 149`
(iii) `15^2 < 252 < 16^2`
add `= 16^2 - 252`
`= 256 - 252= 4`
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