Let $x$ and $y$ be rational and irrational numbers, respectively. Is $x+y$ necessarily an irrational number? Give an example in support of your answer.
Let $x$ and $y$ be rational and irrational numbers, respectively. Is $x+y$ necessarily an irrational number? Give an example in support of your answer.
Yes, $x+y$ is necessary an irrational number.
Let $x=5$ and $y=\sqrt{2}$
Then, $x+y=5+\sqrt{2}=5+1.4142 \ldots \ldots=6.4142 \ldots \ldots$ which is non - terminating and nonrepeating.
Hence, $x+y$ is an irrational number.
Similar Questions
Show that $0.142857142857 \ldots=\frac{1}{7}$
Show that $0.142857142857 \ldots=\frac{1}{7}$
Which of the following is irrational?
Which of the following is irrational?
Express $0 . \overline{4}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$
Express $0 . \overline{4}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$
Represent $\sqrt{20}$ on the number line.
Represent $\sqrt{20}$ on the number line.
Rationalise the denominator of the following:
$\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}}$
Rationalise the denominator of the following:
$\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}}$