NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.4 Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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The Square Root of the Perfect Square

Question: 5 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

Answer:

(i) 525

Square Root of 525 is 22 with remainder41

Since remainder is 41.

Next perfect square number

Hence, number to be added

Hence, the square root of 529 is 23.

(ii) 1750

Square Root of 1750 is 41 with Remainder 69

Since remainder is 69.

Next perfect square number

Hence, number to be added

Hence, the square root of 1764 is 42.

(iii) 252

Square Root of 252 is 15 with Remainder 27

Since remainder is 27.

Next perfect square number

Hence, number to be added

Hence, the square root of 256 is 16.

(iv) 1825

Square Root of 1825 is 42 with Remainder 61

Since remainder is 61.

Next perfect square number

Hence, number to be added

Hence, the square root of 1849 is 43.

(v) 6421

Square Root of 6412 is 80 with remainder12

Since remainder is 12.

Next perfect square number

Hence, number to be added

Hence, the square root of 6561 is 81.