Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$
Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$
$(i )-\sqrt{0.4}=-\frac{2}{\sqrt{10}},$ which is a quotient of a rational and an irrational number and so it is an irrational number.
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}=\sqrt{\frac{4}{25}}=\frac{2}{5},$ which is a rational number.
Similar Questions
Simplify
$3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}}$
Simplify
$3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}}$
Write the following in decimal form and state what kind of decimal expansion each has
$\frac{5}{13}$
Write the following in decimal form and state what kind of decimal expansion each has
$\frac{5}{13}$
Convert following rational numbers in decimal form and state the kind of its decimal expansion
$\frac{25}{8}$
Convert following rational numbers in decimal form and state the kind of its decimal expansion
$\frac{25}{8}$
If $\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}}=a+b \sqrt{30},$ find the value of $a$ and $b$.
If $\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}}=a+b \sqrt{30},$ find the value of $a$ and $b$.
Represent $\sqrt{6}$ on the number line.
Represent $\sqrt{6}$ on the number line.