Math, asked by chiragmendiratp76b4j, 1 year ago

prove that 3+2root 3 is an irrational number

Answers

Answered by SillySam
6
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.

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