Identify whether the given number is a rational or irrational number:
$\frac{\sqrt{12}}{\sqrt{75}}$

Question

Identify whether the given number is a rational or irrational number-displaystyle frac-sqrt-12-sqrt-75-

Toppr Admin · Accepted Answer

Given- -x221A-12-x221A-75-x221A-2-xD7-2-xD7-3-x221A-3-xD7-5-xD7-5-xA0-2-x221A-35-x221A-3 -25Here- both 2 and 5 are integer-Therefore-x221A-12-x221A-75 is a rational number-

Identify whether the given number is a rational or irrational number:√12√75

Given, √12√75=√2×2×3√3×5×5=2√35√3 =25Here, both 2 and 5 are integer.Therefore,√12√75 is a rational number.

Identify whether the given number is a rational or irrational number:
$\frac{\sqrt{12}}{\sqrt{75}}$

Given, $\frac{\sqrt{12}}{\sqrt{75}}$

$= \frac{\sqrt{2 \times 2 \times 3}}{\sqrt{3 \times 5 \times 5}}$
$= \frac{2 \sqrt{3}}{5 \sqrt{3}}$
$= \frac{2}{5}$
Here, both $2$ and $5$ are integer.
Therefore, $\frac{\sqrt{12}}{\sqrt{75}}$ is a rational number.