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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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