Question

prove that 5+2√5 is irrational​

Answer 1

Answer:

answer is 15.3/.14 hope it's helpfull make me as brailiest answer if no so ok

Answer 2

Answer:

Let us assume on the contrary that 5+2√5 is rational.

∴ $5+2\sqrt{5} = \frac{a}{b}$         (where a & b are integers, b≠0)

$2\sqrt{5} = \frac{a}{b}-5\\ 2\sqrt{5} = \frac{a-5b}{b}\\\sqrt{5}= \frac{a-5b}{2b}$

Since, a & b are integers, therefore, $\frac{a-5b}{2b}$ is rational.

∴ √5 is also rational.

But this contradicts the fact that √5 is irrational.

This contradiction has arisen due to wrong assumption that 5+2√5 is rational.

Hence, 5+2√5 is IRRATIONAL.

Hence Proved.

Hope It Helps :)