Question

State true or false:

State which of following real numbers are irrational:
$-8.0,\sqrt{5},\frac{5}{7},-\sqrt{18},\sqrt{32},4.28,\pi ,3,\frac{8}{15},0.075$

Answer: $\sqrt{5},-\sqrt{18},\sqrt{32},\pi$

• A. True
• B. False

Answer 1

The correct option is A True

Rational numbers are those numbers which can be expressed in
the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$

Numbers
which are not rational numbers are called irrational numbers.

From the given set of numbers, $-8.0,\frac{5}{7},4.28,3,\frac{8}{15},0.075$ are clearly
rational numbers are they can be written in $\frac{p}{q}$ form.
Now, $\sqrt{5},-\sqrt{18},\sqrt{32}$ are not rational numbers as they cannot be simplied to $\frac{p}{q}$ form.
Also, $\pi$ is not a rational number.
Hence, the irrational numbers in the given set are $\sqrt{5},-\sqrt{18},\sqrt{32},\pi$