Question

What least number must be subtracted from 6899 to make it a perfect square . What is the new number ? Also find its square root. please answer in detail

Answer 1

$Given \: number \; 6899$

$We \: find \: by \: division \:method :$

8 | 68 99 | 83

×8| 64

_________

163| 499

*× 3| 489

__________

166* | 10

$\blue { Remainder = 10 }$

$This \: means , \:if \: we \: subtract \:10 \:from \\6899. \: We \: get \: a \: perfect \: square .$

$Hence, the \: required \: least \:number \: is \: 10$

$\red{ Required\: perfect \: square } \\= 6899 - Remainder \\= 6899 - 10 \\= 6889 \\= 83^{2} \: \blue { ( Perfect \: square ) }$

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