Question

16) Find the least number which must be subtracted from 271451 to get a perfect
square number also find the square root of the perfect square number. ​

Answer 1

Solution :-

Finding square of 271451 by long division method we get,

5 ) 27 - 14 - 51 ( 5

25

102 ) 214 ( 2

204

1041 ) 1051 ( 1

1041

10

as we can see that, remainder we gets is 10 . Therefore, we can conclude that, if we subtract the remainder from given number it will be a perfect square .

Hence, the least number must be subtracted is 10 and then square root of perfect square number 271441 will be 521 .

Shortcut :-

→ √271451 ≈ 521 .

so,

→ (521)² < 271451 < (522)²

→ 271441 < 271451 < 272484

then,

→ Required number must be subtracted = 271451 - 271441 = 10

therefore, the square root of perfect square number is 521 .

Note :- If asked what number must be added , we have to subtract 271451 from (522²) and then square root will be 522 .

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