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

Solution:

Given numbers are not perfect squares

First find out the square root of the number, then round it off to the next whole number. That number is the next possible perfect square root. So we add the difference between the two to get the perfect square.

(i) The square root of 525 is calculated as

It is evident that 22² < 525

The next perfect square of a whole number is

23² = 529

Hence, the number to be added to 529

= 529 - 525

= 4

The required perfect square is 525 + 4 = 529 whose root is 23

(ii) The square root of 1750 is calculated as

This shows that 41² < 1750

Next perfect square is 42² = 1764

Hence number to be added to 1750

= 1764 - 1750

= 14

The required perfect square is 1750 + 14 = 1764 whose root is 42

(iii) The square root of 252 is calculated as

This shows that 15² < 252

Next perfect square is 16² = 256

Hence number to be added to 252

= 256 - 252

= 4

The required perfect square is 252 + 4 = 256 whose root is 16

(iv) The square root of 1825 is calculated as

This shows that 42² < 1825

Next perfect square is 43² = 1849

Hence number to be added to 1825

= 43² - 1825

= 1849 - 1825

= 24

The required perfect square is 1825 + 24 = 1849 whose root is 43

(v) The square root of 6412 is calculated as

This shows that 80² < 6412

Next perfect square is 81² = 6561

Hence number to be added to 6412 is

= 6561 - 6412

= 149

The required perfect square is 6412 + 149 = 6561 whose root is 81

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

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Video Solution:

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

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.4 Question 5

Summary:

The least numbers that need to be added to the given numbers (i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412 to get a perfect square are (i) 4, (ii) 14, (iii) 4, (iv) 24, and (v) 149 and the square roots are as follows 23, 42, 16, 43 and 81.

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