Question

prove that
$1 \div \sqrt{2} \: is \: irrational$
​

Answer 1

Hey brainly user

Here is your answer

Let us assume that

$\sqrt{2} is \: a \: rational \: number$

Rational number : Which is in the form of p/q where q is not equal to zero and p, q are CO primes

$\sqrt{2} = \frac{p}{q}$

$2 = p { }^{2} \div q {}^{2}$

$2q { }^{2} = p {}^{2}$

It shows that 2 divides psquare and 2 divides p

Let us take p=2 a

$2q { }^{2} = 4a {}^{2}$

$q {}^{2} = 2a {}^{2}$

Here 2 divides q square and 2 divides q

So p, q= 2

It's not possible because these are CO primes

$\sqrt{2} is \: a \:i rrational \ \: number:$

Division with irrational number gives irrational number only

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