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

To do: 

We have to give an example of each of two irrational numbers whose product 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.

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

This implies,

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

Therefore,

$(2\sqrt{2})\times(3\sqrt{3})=(2\times3)(\sqrt{2\times3})$

$=6\times\sqrt{6}$

$=6\sqrt{6}$

$\sqrt{6}$ is an irrational number.    

$\Rightarrow 6\sqrt{6}$ is an irrational number.

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Updated on: 10-Oct-2022

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