An army base has some soldiers, such that when they stand in rows and columns they form a square. More soldiers were added to the camp and now the number of rows and columns increased by 1. If there are 676 soldiers now, how many soldiers were added?

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Solution

The correct option is B
51

Number of rows and columns when there are 676 soldiers = $\sqrt{676}$ = $\sqrt{26 \times 26}$ = 26

$\Rightarrow$ Intial number of rows and columns = 26 -1 = 25 (As one more row and column was added)

$∴$ , initial number of soldiers $25^{2}$ = 625

$∴$ number of soldiers added = 676 - 625 = 51

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An army base has some soldiers, such that when they stand in rows and columns they form a square. More soldiers were added to the camp and now the number of rows and columns increased by 1. If there are 676 soldiers now, how many soldiers were added?

The correct option is B 51 Number of rows and columns when there are 676 soldiers = √676 = √26×26 = 26 ⇒ Intial number of rows and columns = 26 -1 = 25 (As one more row and column was added) ∴, initial number of soldiers 252 = 625 ∴ number of soldiers added = 676 - 625 = 51