Question

classify the following numbers as rational or irrational give reason to support your answer root 3 by 81

Answer 1

√3/81 = √1/27 it is because its non terminating :)

Answer 2

Answer:

$\frac{\sqrt{3}{81}\: is \: irrational$

Step-by-step explanation:

$Let\:us\: assume \:\frac{\sqrt{3}}{81}\\is \:a \:ration$

$\frac{\sqrt{3}}{81}=\frac{a}{b}\\where\:a,b \:are \: Integers\\and \: b≠0$

$\implies \sqrt{3}=\frac{81a}{b}$

$Since,\:a,b \: are \: integers \: \frac{81a}{b}\: is \: rational.\\So,\sqrt{3}\: is \: rational.$

But , √3 is irrational .

This contradicts the our assumption.

Therefore,

$\frac{\sqrt{3}{81}\: is \: irrational$

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