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
Verified
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.
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