Question

Prove that 2√3 + 3 is an irrational number. class 10 real numbers​

Answer 1

Answer:

Lets Assume that 2√3+3 is rational

2√3+3= a/b, where a and b are co-prime integers.

2√3= a/b -3

2√3= a-3b/b

√3= a-3b/2b

Here, a-3b/2b is rational. but this contradicts the fact that √5 is irrational.

Thus, Our Assumption is wrong, i.e., 2√3+3 is an irrational number

Step-by-step explanation: