State whether the following statements are true or false? Justify your answer.
$(i)$ The square of an irrational number is always rational.
$(ii)$ $\frac{\sqrt{12}}{\sqrt{3}}$ is not a rational number as $\sqrt{12}$ and $\sqrt{3}$ are not integers.
State whether the following statements are true or false? Justify your answer.
$(i)$ The square of an irrational number is always rational.
$(ii)$ $\frac{\sqrt{12}}{\sqrt{3}}$ is not a rational number as $\sqrt{12}$ and $\sqrt{3}$ are not integers.
$(i)$ The given statement is false. Consider an irrational number $\sqrt[4]{2}$. Then, its square $(\sqrt[4]{2})^{2}=\sqrt{2},$ which is not a rational number.
$(ii)$ The given statement is false. $\sqrt{\frac{12}{3}}=\sqrt{4}=2,$ Which is a rational number.
Similar Questions
Value of $\sqrt[4]{(81)^{-2}}$ is
Value of $\sqrt[4]{(81)^{-2}}$ is
Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$
$\frac{\sqrt{10}-\sqrt{5}}{2}$
Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$
$\frac{\sqrt{10}-\sqrt{5}}{2}$
If $x=3+2 \sqrt{2},$ then find the value of $x^{2}+\frac{1}{x^{2}}$ and $x^{3}+\frac{1}{x^{3}}$
If $x=3+2 \sqrt{2},$ then find the value of $x^{2}+\frac{1}{x^{2}}$ and $x^{3}+\frac{1}{x^{3}}$
Find three rational numbers between
$\frac{1}{4}$ and $\frac{1}{5}$
Find three rational numbers between
$\frac{1}{4}$ and $\frac{1}{5}$
Simplify:
$\frac{8^{\frac{1}{3}} \times 16^{\frac{1}{3}}}{32^{-\frac{1}{3}}}$
Simplify:
$\frac{8^{\frac{1}{3}} \times 16^{\frac{1}{3}}}{32^{-\frac{1}{3}}}$