Give an example of each of two irrational numbers whose quotient is an irrational number.

To do: 

We have to give an example of each of two irrational numbers whose quotient is an irrational number.

Solution:

A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.

$\sqrt{2}, \sqrt{3}, \sqrt{6}$ are irrational numbers.

This implies,

$4\sqrt{6}, 2\sqrt{3}$ are irrational numbers.

Therefore,

$(4\sqrt{6})\div(2\sqrt{3})=\frac{4\sqrt{6}}{2\sqrt{3}}$

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

$=2\sqrt{2}$

The quotient $2\sqrt{2}$ is an irrational number.    

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Updated on: 10-Oct-2022

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