Find the two numbers which on multiplication with $\sqrt{360}$ gives a rational number. Are these numbers rational or irrational?
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Find the two numbers which on multiplication with $\sqrt{360}$ gives a rational number. Are these numbers rational or irrational?

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SOLUTION —

$\sqrt{360}=\sqrt{2 \times 2 \times 2 \times 3 \times 5}=6 \sqrt{10}$

If we multiply $6 \sqrt{10}$ with $\sqrt{10}$ and 1 .

We get, $6 \sqrt{10} \times \sqrt{10} \times 1=60$

Hence, Numbers are $\sqrt{10}$ and 1 .

Where, 1 is a rational number and $\sqrt{10}$ is an irrational number. 

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