Let $x$ be rational and $y$ be irrational. Is xy necessarily irrational? Justify your answer by an example.
Let $x$ be rational and $y$ be irrational. Is xy necessarily irrational? Justify your answer by an example.
Let $x =0$ (a rational number) and $y=\sqrt{3}$ be an irrational number.
Then, $x y=0(\sqrt{3})=0,$ which is not an irrational number.
Hence, $xy$ is not necessarily an irrational number.
Similar Questions
State whether the following statement is true:
There is a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational. Justify your answer by an example.
State whether the following statement is true:
There is a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational. Justify your answer by an example.
If $\sqrt{2}=1.4142,$ then evaluate $\sqrt{5} \div \sqrt{10}$ correct to four decimal places.
If $\sqrt{2}=1.4142,$ then evaluate $\sqrt{5} \div \sqrt{10}$ correct to four decimal places.
Visualise $-4.126$ on the number line, using successive magnification.
Visualise $-4.126$ on the number line, using successive magnification.
Which of the following is equal to $x$?
Which of the following is equal to $x$?
Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:
$(i)$ $x^{2}=5$
$(ii)$ $\quad y^{2}=9$
$(iii)$ $z^{2}=.04$
$(iv)$ $u^{2}=\frac{17}{4}$
Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:
$(i)$ $x^{2}=5$
$(ii)$ $\quad y^{2}=9$
$(iii)$ $z^{2}=.04$
$(iv)$ $u^{2}=\frac{17}{4}$