Question

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square . Also find the square root of the perfect square so obtained
(i)402, (ii) 1989, (iii) 3250, (iv)825 (v) 4000
A. Least number which must be subtracted : (i)2, (ii)22, (iii)1,(iv)21,(v)52
Square root of the perfect square
(i)20 (ii)34 (iii)55 (iv)26 (v)67
B. Least number which must be subtracted : (i)2, (ii)53, (iii)1,(iv)41,(v)31
Square root of the perfect square
(i)20 (ii)44 (iii)57 (iv)28 (v)63
C. Least number which must be subtracted : (i)6, (ii)22, (iii)50,(iv)31,(v)40
Square root of the perfect square
(i)19 (ii)41 (iii)49 (iv)27 (v)65
D. Least number which must be subtracted : (i)8, (ii)41, (iii)12,(iv)56,(v)4
Square root of the perfect square
(i)19 (ii)22 (iii)37 (iv)26 (v)61

Answer 1

Hint: Find the nearest square to the given numbers and then find the difference between them and solve it and then find the square root.

Complete step-by-step answer:
The given numbers are 402,1989,3250,825,4000

(i) Let us consider the first number 402
    402 is not a perfect square
    The nearest perfect square is 400
    So, 402-2=400
    So, the least number which must be subtracted is 2
    The square root of 400= 20

(ii)Let us consider the second number 1989
     1989 is not a perfect square
     The nearest perfect square is 1936
     So, 1989-1936=53
     So, the least number which must be subtracted is 53
     Now, the square root of 1936 = 44

 (iii) Let us consider the third number 3250
        It is not a perfect square
       The nearest perfect square is 3249
       So, 3250-1=3249
       So, the least number which has to be subtracted is 1
       The square root of 3249=57

 (iv) Let us consider the fourth number 825
         It is not a perfect square
        The nearest perfect square is 784
        So, 825-784=41
        So, the least number which has to be subtracted is 41
         The square root of 784 is 28

  (v) Let us consider the fifth number 4000
         It is not a perfect square
         The nearest perfect square is 3969
         So, 4000-3969=31
         So, the least number which has to be subtracted is 31

      The square root of 3969 is 63.

      So, from this, we can say

      Least number which must be subtracted are (i)2, (ii)53, (iii)1,(iv)41,(v)31 respectively

       Square root of the perfect square are
         (i)20 (ii)44 (iii)57 (iv)28 (v)63 respectively
          So, option B is the correct answer to this question


Note: Whenever solving these type of problems , find out the nearest perfect square by inspection and from that find out the difference between the two numbers and then find out the square root of the perfect square.