Question

prove that 3 + root 5 is irrational number​

Answer 1

To prove that 3+root2 is an irrational number

lets take the opposite i.e 3+root2 is a rational number

hence 3+root2 can be written in the form a/b

hence 3+root2 = a/b

          root2 = 1/3 x a/b

          root2 = a/3b

here a/3b is rational and root2 is irrational

as irrational cannot be equal to rational 

3+root2 is irrational

hoped it helped u

Answer 2

Answer:

HEYA FRIEND HERE IS YOUR ANSWER

Let 3+√5 be rational

then,

3+√5 = p/q

Squaring both the sides

(3+√5)² = (p/q)²

(3)² + 2(3)(√5) + (√5)² = p²/q²

9 + 6√5 + 5 = p²/q²

14 + 6√5 = p²/q²

Transposing 14 to R.H.S.

6√5 = p²/q² - 14

6√5 = p² -14/q²

Transposing 6 to R.H.S.

√5 = p² -14/ 6q²

L.H.S : √5

here √5 is irrational

R.H.S. : p²- 14/ 6q²

here p² - 14/ 6q² is rational

∵ p and q are integers and 6q² is also an integer

∴ it is rational

∵ L.H.S. ≠ R.H.S.

∴It our assumption is wrong

Hence 3+√5 is irrational

HOPE IT HELPS YOU!!