Question

prove that root 2 is an irrational number​

Answer 1

Answer:

Step-by-step explanation:

First lets see what root 2 is

Its a hypotenuse of a right angle triangle with the side and 1 and 1

By using the pythagoras theorm we can get the hypotenuse by squaring the sides and adding them up

therefore 1square +1 square is 2

And then we have to put a root against it

we can say that root 2 is a irrational number because it can be represented in p/q form

Answer 2

let √2is a rational number then it is written in the form of p/q where q is not 0 and p and q has no common factor

then,

√2=p/q

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

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

here 2 factor of 2q square and factor of p square then 2 is also the factor of p

then,

$p = nx \: \: \: \: \: \: ...... (1)$

${p}^{2} = {2}^{2} {x }^{2}$

${2q}^{2} = {2}^{2} {x}^{2}$

${q}^{2} = {2x}^{2}$

here 2 is factor of 2x square and q square

then 2 is also the factor of q

thus,

our statement is wrong

and 2 is irrational number

2nd method is by the remark:-

square root of any prime number is irrational number