Classify the following number as rational and irrational. Give reasons to support your answer..

Foundation

Mathematics Foundation

Properties of Real Number

Irrational Number

Rational Numbers

Question

Classify the following number as rational and irrational. Give reasons to support your answer. $\frac{2}{3} \sqrt{6}$ .

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

We have a rational number $\frac{2}{3}$ and irrational number $\sqrt{6}$ .

As per the theorem the product of both rational and irrational number is an irrational number.
Thus,

\frac{2}{3} \sqrt{6}

is irrational.