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

To do: 

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

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

This implies,

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

Therefore,

$(4\sqrt{2})\div(2\sqrt{2})=(4\div2)(\sqrt{2}\div\sqrt{2})$

$=2\times1$

$=2$

The quotient $2$ is a rational number.   

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Updated on: 10-Oct-2022

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