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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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