Question

prove it 5+2√3 is irrational​

Answer 1

Answer:

5+2√3 is irrational number.

Step-by-step explanation:

5+2√3:-

First we assume that 5+2√3 is a rational number i.e., in the form of a/b. 'a' and 'b' are co primes.

so,

5+2√3 =a/b

Squaring on both sides

(5+2√3)² =(a/b)²

25+12+20√3 = a²/b²

37+20√3 = a²/b²

20√3 = a²/b²−37

20√3 = a²-37b²/b²

√3 = a²-37b²/20b²

conclusion:-

Finally, we got the answer in rational form.So,5+2√3 is rational number. But,this contradicts. This happens because of our assumption. our assumption is wrong. So 5+2√3 is an irrational number..