Question

Q2 prove that root 7 is an irrational number.

Answer 1

To prove root 7 is irrational number we first assume that it is a rational number.
So, a rational number  can be represented in the form of p/q where p and q are integers and q is not equal to zero.

root 7 = p/q
7 = p square/ q square

p square = 7/ q square

q square divides 7, so q divides 7.
Now let p = 7m

p square = 7/ q square
7m the whole square = 7/ q square
49 m square = 7/q square
q square = 7m/7

so p square divides 7 and p divides 7

hence p and q have common factor other than one that is 7 hence root 7 is irrational.