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Question

Is this number $${ 7\sqrt { 5 }  }$$ is irrational or rational?


Solution

Let $$7\sqrt{5}$$ be rational

$$7\sqrt{5}=\dfrac{p}{q} \left(\dfrac{p}{q} \text{is a rational }\right)$$ 

$$\sqrt{5}=\left(\dfrac{p}{q}\right)\times \dfrac{1}{7}$$

here $$\sqrt{5}$$ is irrational 

but it is equal to a rational number this contradicts that $$7\sqrt{5}$$ is a rational number.

hence $$7\sqrt5$$ is a irrational number

Mathematics

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