State True/ False:

$21$ is an irrational number.

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True

False

answer is A.

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Detailed Solution

The given number is

\sqrt{21}

.
We know that,
A number which can’t be expressed as a terminating decimal or recurring decimal and fractional form is called irrational.
A rational number is a number that can be in the form

p q

, where p and q are integers and q is not equal to zero.
Here we have,

= 21 = 7 × 3 = 3 × 7

We cannot further simplify

3

and

7

in the form

p q

, q

≠

0
Hence,

21

is an irrational number.
Thus, the given statement is true.
Therefore, option 1 is correct.

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