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State true or false:
$3 - \sqrt{5}$ is a rational number.

see full answer

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True

False

answer is B.

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Detailed Solution

We have to find whether

3 - \sqrt{5}

is a rational number.
Suppose

3 - \sqrt{5}

is a rational number.
Let

3 - \sqrt{5} = x

where

x

is a rational number.

\Rightarrow 3 - x = \sqrt{5}

Since

x

is a rational number,

3 - x

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, the given statement is false.
The correct statement would be that

3 - \sqrt{5}

is an irrational number.
Hence, option 2 is correct.

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