Question

Show that √2 is irrational, and hence prove that 11 - 15√2 is irrational​

Answer 1

Answer:

let us assume that √2 is a rational number.

so it can be expressed in the form of p/q, where p and q is co prime integers and q equal to not zero.

=√2=p/q

on square both side we get ,

=2= p square/ q square

5p square= p square---------(1)

so 2 divides p

p is a multiple of 2

p=2m

p square=4m square--------(2)

from equation 1 and 2 we get,

2q square = 4m square.

q square =2m square.

q square is a multiple of 2

q is a multiple of 2

hence p and q have a common factor 2. This contradiction our assumptions that they are co Prime's . Therefore p/q is not a rational number

√2 is an irrational number.