Question

Hi Guys...!!!

Prove 1/√2 is irrational ?....☺

In easy method

Answer 1

Let us assume 1/√2 as rational

Let us multiply √2 up and down.

So, √2/2 = a/b ( a and b are integers and b not equal to 0)

√2 = a*2/b

=integer * 2 / integer

= rational

But this contradicts with the fact that root 2 is irrational

Therefore our assumption is wrong, 1/root2 is irrational

:)

Answer 2

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Here is your answer...✨✨✨

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To prove 1/√2 is irrational

Let us assume that √2 is irrational

1/√2 = p/q ( where p and q are co prime )

q/p = √2

q = √2p

Squaring on both sides

${q}^{2} = 2 {p}^{2}$
---------------------------(1)

By theorem
q is divisible by 2

Since, q = 2c ( where c is an integer )

Putting the value of q in equation (1)


$2 {p}^{2} = {q}^{2} = 2 {c}^{2} = 4 {c}^{2}$
${p}^{2} = 4 {c}^{2} \div 2 = 2 {c}^{2}$
${p}^{2} \div 2 = {c}^{2}$
By theorem p is also divisible by 2

But p and q are co prime

This is a contradiction which has arisen due to our wrong assumption....


Since, 1/√2 is irrational....


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