Question

Show That 3✓2 Is Irriational ​

Answer 1

Let us assume , to the contrary , that 3√2 is rational

$\to3 \sqrt{2} = \frac{a}{b} \\ \\ \to \sqrt{2} = \frac{a}{3b}$

Since 3 , a and b are integers , $\frac{a}{3b}$ Is rational , So √2 is rational

But The contradicts the fact that √2 is irrational

So , We conclude that 3√2 is irrational

Answer 2

GIVEN : A number i.e. 3√2

PROVE : 3√2 is an irrational number.

PROOF : Let us assume that 3√2 is an rational number.

→ 3√2 = $\dfrac{a}{b}$

Here.. a and b are co-prime numbers.

→ √2 = $\dfrac{a}{3b}$

Now..

$\dfrac{a}{3b}$ is rational number.

So, √2 is also a rational number.

But we know that √2 is irrational number.

This means that, our assumption is wrong.

3√2 is an irrational number.

_______ [ PROVED ]

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