Question

State whether the following statement is True of False ?Justify your answer.$\frac{\sqrt{72}}{\sqrt{2}}$ is not a rational number as $\sqrt{72}and\sqrt{2}$ are not integers.

• A. True
• B. False

Answer 1

The correct option is B False

Irrational Number / Irrational Number = May or may not be an Irrational Number

$\sqrt{2}=1.414\dots ,\sqrt{3}=1.732\dots ,\sqrt{5}=2.236\dots$

$\sqrt{2}\sqrt{3}=1.732\dots 1.414\dots =1.2234\dots$

We see the pattern which we get from dividing these numbers is non-repeating and non terminating. So this makes the entire number an irrational number. But,

$5\sqrt{5}\sqrt{5}=5$

Here, $5$ is a rational number. Because of this, we say that when we divide two irrational numbers we may or may not get an irrational number.

In given question,

$\frac{\sqrt{7}2}{\sqrt{2}}$ is a irrational number.

Since $\frac{\sqrt{7}2}{\sqrt{2}}=\pm \frac{6}{1}$

We know that the division of two irrational no. may or may not be an irrational number.

The given statement is false.