Question

smallest number which when added to 7669 make the resultant a perfect square. correct answer with proper steps

Answer 1

Solution - ​​

Note - At first, we need to find the sq. root of 7669 by long division method

[Refer to the attachment]  

As, (87)² < 7669 < (88)²  

Perfect sq. = 88² = 7,744  

Smallest no. To be added  

= 7,744 - 7,669  = 75  

∴ Perfect sq. = 7,744  

∴ Smallest no. to be added = 75  

Explaination -  

The question had said that the given number 7,669 is not a perfect sq.  

So, the question had asked for the perfect sq. and by calculating the sq. root of 7,669 we found that it is not a perfect sq. and we also found that (87)² which is 7,569 is smaller than 7,669  

So, we can take the next perfect sq. i.e. (88)² which is 7,744  

∴ 7,744 is the perfect sq. and it's sq. root is 88  

The question had also asked for the smallest no. which when added to 7,669 it turns into a perfect sq.  

So we know that the perfect sq. is 7,744...  

So, just subtract 7,744 with 7,669 and we got 75 which is the smallest no. to be added  

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