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Is the statement true?

The $5 − 2$ is an irrational number.

see full answer

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True

False

answer is A.

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Detailed Solution

Given,
The irrational number is

5 − 2

.
As we know,
The real numbers which cannot be expressed in the form of

p q

, where

p

and

q

are integers and

q ≠ 0

is an irrational number.
Let

x

be the rational number, where,

⇒ x = 5 − 2

⇒ 2 = 5 − x

x

is rational number so

5 − x

is also a rational number.
Therefore

2

is a rational number.
This is the contradiction as

2

is an irrational number.
So,

5 − 2

must be an irrational number.
Thus,

5 − 2

is an irrational number.
Thus, the above statement is true.
Therefore, option(1) is the correct answer.

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