Question

Prove that √2 is irrattional​

Answer 1

Answer:

To prove that the square root of 2 is irrational is to first assume that its negation is true. Therefore, we assume that the opposite is true, that is, the square root of 2 is rational. ... So, 2 = a b \sqrt 2 = {\Large{{a \over b}}} 2 =ba where a and b are integers but b ≠ 0 b \ne 0 b=0.

Answer 2

√2

Method Of Contradiction

let √2 be a rational number that is it can be expressed in the form of p/q where p and q are integers and q ≠0

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

$\sqrt{2} q = p$

squaring b/s

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

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

hence , we can say that p is the multiple of 2

Let p = 2m

$2 {q}^{2} = {(2m)}^{2}$

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

${q}^{2} = \frac{4 {m}^{2} }{2}$

${q}^{2} = 2 {m}^{2}$

hence , we can say that q is also a multiple of 2

but , p and q were co - primes

hence , we can say our contradiction is wrong .

.°. √2 is irrational number

hence prooved