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State true or false:
$7 \sqrt{5}$ is an irrational number.

see full answer

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True

False

answer is A.

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Detailed Solution

We have to find whether

7 \sqrt{5}

is an irrational number.
Let

7 \sqrt{5} = x

where is a rational number.

\Rightarrow \frac{x}{7} = \sqrt{5}

Since

x

is a rational number,

\frac{x}{7}

is also a rational number.
Then

\sqrt{5}

is a rational number, but it is known that

\sqrt{5}

is an irrational number.
Therefore, our assumption is wrong.
Thus, it is true that

7 \sqrt{5}

is an irrational number.
Hence, option 1 is correct.

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