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
Simplify the following:
$4 \sqrt{12} \times 7 \sqrt{6}$
Simplify the following:
$4 \sqrt{12} \times 7 \sqrt{6}$
prove that.
$\left(1^{3}+2^{3}+3^{3}+4^{3}+5^{3}\right)^{\frac{1}{2}}$ $=\left(1^{3}+2^{3}+3^{3}+4^{3}\right)^{\frac{1}{2}}+\left(5^{3}\right)^{\frac{1}{3}}$
prove that.
$\left(1^{3}+2^{3}+3^{3}+4^{3}+5^{3}\right)^{\frac{1}{2}}$ $=\left(1^{3}+2^{3}+3^{3}+4^{3}\right)^{\frac{1}{2}}+\left(5^{3}\right)^{\frac{1}{3}}$
A rational number between $\sqrt{2}$ and $\sqrt{3}$ is
A rational number between $\sqrt{2}$ and $\sqrt{3}$ is
Represent $\sqrt{5}$ on the number line.
Represent $\sqrt{5}$ on the number line.
Find three different irrational numbers between the irrational numbers $\sqrt{2}$ and $\sqrt{5}$.
Find three different irrational numbers between the irrational numbers $\sqrt{2}$ and $\sqrt{5}$.