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Irrational Numbers

Assertion A8 ...

Question

Assertion (A)
$\sqrt{8}$ is an irrational number.
Reason (R)
If m is a natural number which is not a perfect square, then $\sqrt{m}$ is irrational.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Solution

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

$\sqrt{8} = \sqrt{2 \times 2 \times 2} = 2 \sqrt{2}$ = an irrational number and not a perfect square
So, Reason (R) is a correct explanation of Assertion (A).

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Reason (R)
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\frac{ar (∆ A B C)}{ar (∆ D E F)} = \frac{A B^{2}}{D E^{2}} = \frac{B C^{2}}{E F^{2}} = \frac{A C^{2}}{D F^{2}} .

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Reason (R)
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