Question

prove that 5+3√2 is an irrational number​

Answer 1

Answer:

Let us assume the contrary.

i.e; 5 + 3√2 is rational

∴ 5 + 3√2 =

a

b

, where ‘a’ and ‘b’ are coprime integers and b ≠ 0

3√2 =

a

b

– 5

3√2 =

a−5b

b

Or √2 =

a−5b

3b

Because ‘a’ and ‘b’ are integers

a−5b

3b

is rational

That contradicts the fact that √2 is irrational.

The contradiction is because of the incorrect assumption that (5 + 3√2) is rational.

So, 5 + 3√2 is irrational.

please make me Brainlist answer

Answer 2

Answer:

Let us consider that 5+3√2is rational

⇒5+3√2=p/q

where

p and q are co prime

q≠0

p and q are integers

5+3√2=p/q

⇒3√2=p/q-5

⇒3√2=p-5q/q

⇒√2=p-5q/3q

√2 is irrational but p-5q/3q is rational

This contradicts that our supposition is wrong

∴ 5+3√2 is irrational

Step-by-step explanation: