Question

Proove root 2 is irrational no. do fast plz

Answer 1

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Here is your answer
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Let √2 is rational number

√2 = $\dfrac{a}{b}$

[Here a and b are co-prime numbers]

b√2 = a

Squaring on both sides

2b² = a² ....(1)

b² = $\dfrac{{a}{^2}}{2}$

Here 2 divide a² and 2 divide a also.

Now....

a = 2c

[Here c is integer]

Squaring on both sides

a² = 4c²

2b² = 4c² [From (1)]

b² = 2c²

c² = $\dfrac{{b}^{2}}{2}$

Here 2 divide b² and 2 divide b also.

Both a and b are co-prime numbers. And 2 divides both of them.

So, our assumption is wrong.

√2 is irrational number.

Hence proof.