Question

Prove that 3+2√5 is irrational​

Answer 1

Answer:

3+2√5 is

=7.47213595499958

Answer 2

Given :-

• $3 + 2 \sqrt{5}$

To Prove :-

• $3 + 2 \sqrt{5} \: is \: irrational$

Solution :-

Let us assume that it is rational,

So, it can be written in the form a/b

Where, a and b both are co - prime numbers and b is not equal to 0

$= > 3 + 2 \sqrt{5} = \frac{a}{b} \: \: \: \\ = > 2 \sqrt{5} = \frac{a - 3b}{b} \\ = > \sqrt{5} = \frac{a - 3b}{2b}$

$this \: shows \: that \: \frac{a - 3b}{2b} \: is \: irrational$

But we know that under root 5 is irrational.

Hence, our assumption was wrong.

Therefore,

$3 + 2 \sqrt{5} \: is \: irrationl$

Hope the answer helps you phirend ;)