Question

Show that 2 - √13 is an irrational number.​

Answer 1

Answer:

Step-by-step explanation:

let 2- root 13 be a rational number

2- root13=p/q              {represents as p/q-------------1

                                     q does not equal to 0

                                      p and q have no common factor except 1}

squaring both sides,

(2- root 13)^2=p^2/q^2

4-13=p^/2/q^2

-11=p^2/q^2

-11q^2=p^2---------2

p^2 is a multiple of -11

p is also a multiple of -11

let p=-11

(-11m)^2=-11q^2

121m^2=-11q^2

-11m^2=q^2

q^2 is also a factor of -11

q is a factor of -11

hence our assumption is wrong

2- root 13 is not a rational number

2- root 13 is an irrational number