 Questions & Answers    Question Answers

# 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) 4000A. Least number which must be subtracted : (i)2, (ii)22, (iii)1,(iv)21,(v)52Square root of the perfect square(i)20 (ii)34 (iii)55 (iv)26 (v)67B. Least number which must be subtracted : (i)2, (ii)53, (iii)1,(iv)41,(v)31Square root of the perfect square(i)20 (ii)44 (iii)57 (iv)28 (v)63C. Least number which must be subtracted : (i)6, (ii)22, (iii)50,(iv)31,(v)40Square root of the perfect square(i)19 (ii)41 (iii)49 (iv)27 (v)65D. Least number which must be subtracted : (i)8, (ii)41, (iii)12,(iv)56,(v)4Square 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.
Bookmark added to your notes.
View Notes
Least Square Method  How to Find Square Root of a Number  ICSE Full Form  Square Root of Decimal Number  Simplify Square Roots  How to Find Square Root  Squares and Square Roots  How to Find The Median?  Square Root of 10  Fractions on the Number Line  