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

(i) 525
Since remainder is 41. Therefore 22²
Next perfect square number 23² = 529
Hence, number to be added = 529 – 525 = 4
∴ 525+4=529
Hence, the square root of 529 is 23.

(ii) 1750
Since remainder is 69. Therefore 41²<1750
Next perfect square number 42²=1764
Hence, number to be added = 1764 – 1750 = 14
∴ 1750+14=1764
Hence, the square root of 1764 is 42.

(iii) 252
Since remainder is 27. Therefore 152 < 252
Next perfect square number 162 = 256
Hence, number to be added=256-252=4
∴ 252+4=256
Hence, the square root of 256 is 16.

(iv) 1825
Since remainder is 61. Therefore 42²<1825
Next perfect square number 43² = 1849
Hence, number to be added = 1849 – 1825 = 24
∴ 1825 + 24 = 1849
Hence, the square root of 1849 is 43.

(v) 6412
Since remainder is 12. Therefore 80²<6412
Next perfect square number 81²=6561
Hence, number to be added = 6561 – 6412 = 149
∴ 6412 + 149 = 6561
Hence, the square root of 6561 is 81.

Class 8 Maths Chapter 6 Exercise 6.4 Solution in Video

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