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A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5?

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A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5?
1). 1
2). 2
3). 3
4). 4


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3 vote
Answered by on | Votes 3 |

Let the number be x

From given data-

Number when divided by 5 leaves a remainder 3

∴ x = 5q + 3       → dividend= divisor× quotient+ remainder

When square of number is divided by 5

∴ (5q+3)2 ÷ 5

⇒ (25q2 + 30q + 9) ÷ 5     → (a + b)2 = a2 + 2ab + b2

⇒ [5(5q2 + 6q + 1) + 4] ÷ 5

Here we can notice that when divided by 5 square of that number leaves 4 as a remainder

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