Question

PROVE THAT 3+2V3 is irrational. ​

Answer 1

Step-by-step explanation:

step:1

3+2√3 =A/B

step:2

3 goes to RHS → 2√3 = A/B-3

→ 2√3 = A-3B/B

step:3

2 goes to RHS →√3=A-3B/2B

GIVEN THAT √3 IS AN IRRATIONAL NUMBER

SO, 3+2√3 IS AN IRRATIONAL NUMBER

HOPE IT HELPS YOU MARK AS BRAINLIEST ANS

Answer 2

SOLUTION :-

$\dashrightarrow$Let is 3+2√3 rational.

$\dashrightarrow$Therefore,we can find two integers a, b (b$\cancel{=}$0) such that,

$\dashrightarrow$ 3+2√5 = a/b

$\dashrightarrow$2√5 = a/b - 3

$\dashrightarrow$ √5 = ½(a/b -3)

$\dashrightarrow$Since, a and b are integers ,½(a/b -3) will also be rational and therefore , √5 is rational.

$\dashrightarrow$ This contradicts the fact that √5 is rational, Hence, our assumption that 3+2√5 is rational is false.

$\dashrightarrow$ Therefore, 3+2√3 is irrational.

Answer by :- Rajsingh24.