Question

prove that 3+2root 3 is an irrational number

Answer 1

Heya mate,Here is ur answer

Let 3 +2√3 be a rational number.

Then,

3+2√3=a/b ( where a and b are co- prime number and b≠0)

$2 \sqrt{3} = \frac{a }{b} - 3$

$2 \sqrt{3} = \frac{a - 3b}{b}$


$\sqrt{3} = \frac{ \frac{a - 3b}{b} }{2}$


But √3 is an irrational number.

This contradicts our supposition that 3+2√3 is rational number.

So, 3+2√3 is an irrational number.

==========================

Warm regards

@Laughterqueen

Be Brainly ✌✌✌