Question

find the following is rational or irrational by contradiction method?

Answer 1

\[\sqrt{2}+3\]

Answer 2

@cwrw238

Answer 3

I don't know the contraction method but this would be irrational
when a number cannot be expressed as a ratio of integers its irrational

Answer 4

i knew it

Answer 5

i want method

Answer 6

@sreekar369

Answer 7

wait 15min

Answer 8

*following

Answer 9

wow "An indirect proof is also called a proof by contradiction"

Answer 10

@sreekar369

Answer 11

lets take \[\sqrt{2}+3\] as rational
so,we find integers a and b (b is not equal to 0) such tht a/b=\[\sqrt{2}+3\]
=>a/b-3=\[\sqrt{2}\]
=>a-3b/b=\[\sqrt{2}\]
since a,b,3 are integers it is a rational no therfore \[\sqrt{2}\] is a rational no
but it contradicts fact tht \[\sqrt{2}\] is a irrational
so our assumption tht \[\sqrt{2}+3\] is a rational no
so \[\sqrt{2}+3\] is a rational

Answer 12

@sikinder

Answer 13

this implies that 2 is a factor of a^2. Therefore 2 is also a factor of a. Thus a can be written as 2c.