Question

I have to prove that sqrt 11 is irrational, which I have done, ..Is sqrt11 + 3 irrational, please prove?????? Does my head in I tell you :)

Answer 1

\[\sqrt{11}+3\]?

Answer 2

prove it is irrational by using proof by contradiction

Answer 3

I am a bit lost with the plus 3 new to this

Answer 4

suppose \(\sqrt{11}+3\) is rational

Answer 5

then

\[\sqrt{11}+3=\frac{a}{b}\]

a,b integers

Answer 6

then \[\sqrt{11}=\frac{a}{b}-3\]

Answer 7

still with you :)

Answer 8

\[\frac{a}{b}-3\] is a rational number

but \[\sqrt{11}\] is not

this is a contradiction


thus \(\sqrt{11}+3\) is irrational

Answer 9

Is that all I need to say?

Answer 10

what else would you need to add?

Answer 11

ahhhhh because regardless you are still dealing with an irrational number and nothing will change that?

Answer 12

unless you had alot of time on your hands LOL

Answer 13

Is this a correct assumption?