Question

Prove that 3√2/4 is an irrrational numbers

Answer 1

Answer

To prove ,

$\rm \frac { 3 \sqrt2 } { 4 }$ is an irrational number.

Proof,

Let us assume, to the contrary, that $\rm \frac { 3 \sqrt2 } { 4 }$is rational.

Then, there exist co-prime positive integers' a 'and 'b' such that,

⇛ $\rm \frac { 3 \sqrt2 } { 4 } = \frac { a } { b }$

⇛ $\rm 3 \sqrt2 = \frac { 4a } { b }$

⇛ $\rm \sqrt2 = \frac { 4a } { 3b }$

Here we got that $\rm \sqrt2$ is rational as here it is in the form of p/q where $\rm q \neq 0$

This contradicts the fact that $\rm \sqrt2$ is an irrational number.

So our assumptions were wrong

Hence $\rm \frac { 3 \sqrt2 } { 4 }$ is a irrational number

Answer 2

Step-by-step explanation:

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