Question

Find which of the variables $x$,$y$, $z$and $u$ represent rational numbers and which irrational numbers:

$x^2=5$

Answer 1

Determine if the given number is rational or irrational.

Given : $x^2=5$

On taking the square root of both sides we get,

$\Rightarrow x=\pm \sqrt{5}$

We know that, the real numbers which cannot be expressed in the form of $\frac{p}{q}$, where$p$ and$q$ are integers and $q\ne 0$ are known as irrational numbers.

$\pm \sqrt{5}$ cannot be represented in $\frac{p}{q}$ form with the above conditions because it is an irrational number.

So,$x=\pm \sqrt{5}$ is an irrational number.

Hence, $x$ is an irrational number.