Question

Which of the following numbers have an irrational number square root?

• A. $625$
• B. $6025$
• C. $3025$
• D. $1225$

Answer 1

The correct option is B $6025$

Concept:
We know that square root of a non-perfect square is an irrational number.

Square root of $625=\sqrt{25\times 25}=25$
$\Rightarrow 25$ is a rational number.

Square root of $6025=\sqrt{5\times 5\times 241}=5\sqrt{241}$
$\because 241$ is not a perfect square hence $\sqrt{241}$ is an irrational number.

Square root of $3025=\sqrt{5\times 5\times 11\times 11}=55$
$\Rightarrow 55$ is a rational number.

Square root of $1225=\sqrt{5\times 5\times 7\times 7}=35$.
$\Rightarrow 35$ is a rational number.

All are rational numbers except square root of $6025=5\sqrt{241}$