Question : When a certain number is divided by 65, the remainder is 56. When the same number is divided by 13, the remainder is $x$. What is the value of $\sqrt{5x-2}$?
Option 1: $2 \sqrt{7}$
Option 2: $\sqrt{13}$
Option 3: $2 \sqrt{2}$
Option 4: $3 \sqrt{2}$
Correct Answer: $3 \sqrt{2}$
Solution :
Given: When a certain number is divided by 65, the remainder is 56.
When the same number is divided by 13, the remainder is $x$.
Since 65 is divisible by 13, the required remainder is the remainder when 56 is divided by 13.
Divide 56 by 13, we get the remainder $x=4$.
The value of $\sqrt{5x-2}$
$=\sqrt{5\times 4-2}$
$=\sqrt{20-2}=\sqrt{18}=3 \sqrt{2}$
Hence, the correct answer is $3 \sqrt{2}$.
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