State whether the following statements are true or false. Justify your answers.
$(i)$ Every irrational number is a real number.
$(ii)$ Every point on the number line is of the form $\sqrt{m}$,where $m$ is a natural number.
$(iii)$ Every real number is an irrational number.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) $(i)$ True; the set of real numbers consists of both rational and irrational numbers. Therefore,every irrational number is a real number.
$(ii)$ False; negative numbers on the number line cannot be expressed as the square root of any natural number $m$,as the square root of any natural number is always non-negative.
$(iii)$ False; real numbers include both rational and irrational numbers. For example,$2$ is a real number but it is a rational number,not an irrational number.

Explore More

Similar Questions

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$?

Are the square roots of all positive integers irrational? If not,give an example of the square root of a number that is a rational number.

Are the following statements true or false? Give reasons for your answers.
$(i)$ Every whole number is a natural number.
$(ii)$ Every integer is a rational number.
$(iii)$ Every rational number is an integer.

Find the values of:
$(i)$ $64^{\frac{1}{2}}$
$(ii)$ $32^{\frac{1}{5}}$
$(iii)$ $125^{\frac{1}{3}}$

Visualize $4.\overline{26}$ on the number line,up to $4$ decimal places.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo