Is the statement true?The 3 2 is irrational number.

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Is the statement true?

The $32$ is irrational number.

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True

False

answer is A.

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Detailed Solution

Given,
The irrational number is

32

.
Let’s assume that

32

is rational.
So, we can find integers

a

and

b

such that,

⇒ 32 = a b

Where

a

and

b

are co-prime as their H.C.F is 1.

⇒ 2 = a 3 b

Since,

a

and

b

are integers.
Therefore,

a 3 b

is a rational number.
Thus,

2

is a rational number.
But this contradicts the fact that

2

is an irrational number.
Hence, assumption is wrong that

32

is rational.
Hence,

32

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

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