Question

show that 3 + 5 root 2 is an irrational number​

Answer 1

${ { \huge{ \bold{Heya \: Mate!}}}}$

${ \red{ { \bold{To\: Prove }}}}$] ➭3 + 5√2 is irrational

We shall prove this by the method of contraction . So let us assume to the contrary that the given number is rational such that it can be written as -

→$3 + 5 \sqrt{2} = r \\ \\ 5 \sqrt{2} = r \: - 3 \\ \\ \sqrt{2} = \frac{r - 3}{5}$

Now we know that √2 is an irrational number . So the R.H.S can't be rational or else the equation becomes false!

Hence our assumption is wrong.

•°• ${{{\bold{Hence \: It \: is \:Irrational \: Number }}}}$

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Answer 2

let 3+5√2 is a rational no.

so we can write this no. in the form of p/q

→3+5√2=p/q

→5√2=p/q-3

→5√2=(p-3q)/q

→√2=(p-3q)/5q

but √2 is not a rational number

hence it contradicts the fact that √2 is a rational no.

hence 3+5√2 is a irrational number.

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