Question

show that 32 is irrational ?​

Answer 1

Answer:

32 is a rational number. please correct the question

Answer 2

The irrational numbers are the numbers that cannot be expressed as a fraction.

Explanation:

• The irrational numbers are the numbers that cannot be expressed as a fraction.
• They are non-terminating and non-repeating decimals.
• For example : 1.3452334344....., π,  $\sqrt{2}$, etc.

The given expression is $\sqrt{32}$

It can be represented as : $\sqrt{32}=\sqrt{2^5}=\sqrt{2^4\cdot 2}=\sqrt{(2^2)^2\cdot2}= 2^2\sqrt{2}=4\sqrt{2}$

Since , $\sqrt{2}=1.41421356237.....$ which is a non-terminating and non-repeating decimal, i.e. $\sqrt{2}$ is an irrational number.

And product of a rational and irrational is an irrational number that means

$4\sqrt{2}$ is irrational .

i.e. $\sqrt{32}$ is irrational .

Hence, proved.

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