If p is prime, then p is an ____ number.

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If $p$ is prime, then $\sqrt{p}$ is an ____ number.

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Detailed Solution

p

is prime, then

\sqrt{p}

is an irrational number.
Since, we know that prime numbers are those which are never perfect squares and not divisible by any other number except by itself.
which are

2, 3, 5, 7, . . .

Clearly, if

p

is prime then

\sqrt{p}

is an irrational number.
Therefore, the correct answer is irrational.

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