Question

show that 3root 2 is irrational​

Answer 1

Step-by-step explanation:

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Answer 2

To prove:

$3 \sqrt{2} \: is \: irrational$

Proof:

Let us assume that

$3 \sqrt{2 } \: is \: rational$

Hence,

$3 \sqrt{2}$

can be written in the form of-

$\frac{a}{b}$

where a and b (b not equal to 0) are co-prime......

Hence,

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

$\sqrt{2} = \frac{1}{3} \times \frac{a}{b}$

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

Here,

$\frac{a}{3b}$

is a rational number......

But,

$\sqrt{2}$

is irrational....

Since, Rational is not equal to Irrational

This is a contradiction

.: Our assumption is incorrect

Hence,

$3 \sqrt{2}$

is irrational

$\huge \boxed{ \text \color{red}{hence \: proved}}$