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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.

4.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

 

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(i)    402 :-     It can be seen that 2 is remainder. So we will subtract 2 from 402. 

                      The required number is 400 and its square root is 20.                    (ii) 1989 :-       It can be seen that 53 is remainder here. So we will subtract 53 from 1989 in order to make it a perfect square. 

                      The required number is 1936 and its square root is 44.   

 (iii) 3250 :-    It can be seen that 1 is remainder. So we will subtract 1 from 3250. 

                      The required number is 3249 and its square root is 57.

(iv)  825 :-     It can be seen that 41 is remainder. So we will subtract 41 from 825 to make it a perfect square number. 

                    The required number is 784 and its square root is 28.(v) 4000 :-     It can be seen that 31 is remainder here. So we will subtract 31 from 4000. 

                     The required number is 3969 and its square root is 63. 

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