Question

prove that 2/ 5√3 is irrational​

Answer 1

Step-by-step explanation:

Let 2 + 5√3 be rational.

Let 2 + 5√3 be rational.

∴ 2 + 5√3 = p/q ; p, q are integers, q ≠ 0

Let 2 + 5√3 be rational.

∴ 2 + 5√3 = p/q

p, q are integers, q ≠ 0

⇒ √3 = (p/q - 2) ÷ 5

Let 2 + 5√3 be rational.

∴ 2 + 5√3 = p/q

p, q are integers, q ≠ 0

⇒ √3 = (p/q - 2) ÷ 5√3 = (p - 2q)/5q

Let 2 + 5√3 be rational.

∴ 2 + 5√3 = p/q

p, q are integers, q ≠ 0

⇒ √3 = (p/q - 2) ÷ 5√3 = (p - 2q)/5q

LHS is irrational and RHS is rational which is a contradiction.

Let 2 + 5√3 be rational.

∴ 2 + 5√3 = p/q

p, q are integers, q ≠ 0

⇒ √3 = (p/q - 2) ÷ 5√3 = (p - 2q)/5q

LHS is irrational and RHS is rational which is a contradiction.

∴ 2 + 5√3 is irrational.

Hence Proved