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Question

# Find the least number which must be added to 306452 to make it a perfect square.

A

345

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B

465

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C

464

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D

324

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Solution

## The correct option is C 464 We use long division method to find the square root of 306452. For that, we will group 2 numbers from right to left and then proceed with the division. 5535¯¯¯¯¯¯30 ¯¯¯¯¯¯64 ¯¯¯¯¯¯52−25105 564 −5251103 3952 −3309 643 From above, it is clear that given number 306452 is greater than (553)2 i.e.,5532<306452<306916(i.e.5542) Therefore, if we add 306916 - 306452 = 464 to 306452, then the sum 306452 + 464 will be a perfect square. So, the required least number is 464

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