Question

is √12/√75 a rational Number

Answer 1

$\sqrt{12} = \sqrt{3 \times 4} = \sqrt{3} \times \sqrt{4} \\ = \sqrt{3} \times 2 = 2 \sqrt{3} \\ \\ \sqrt{75 } = \sqrt{3 \times 25} = \sqrt{3} \times \sqrt{25} \\ = \sqrt{3} \times 5 = 5 \sqrt{3} \\ \\ \frac{ \sqrt{12} }{ \sqrt{75} } = \frac{2 \sqrt{3} }{5 \sqrt{3} } = \frac{2}{5}$

Which is a rational number...Hence given number is a rational number