# Prove that of the Numbers Sqrt(3) + Sqrt(5) is Irrational: - Mathematics

Prove that of the numbers sqrt(3) + sqrt(5) is irrational:

#### Solution

Letsqrt(3) + sqrt(5) be rational.
∴sqrt(3) + sqrt(5) = a, where a is rational.
∴ sqrt(3) = a - sqrt(5)               ….(1)
On squaring both sides of equation (1), we get
3 = (a - sqrt(5))^2 = a^2 + 5 - 2sqrt(5a)
⇒ sqrt(5) = (a^2+2) /(2a)
This is impossible because right-hand side is rational, whereas the left-hand side is irrational.
Hence,sqrt(3) + sqrt(5)  is irrational.

Concept: Concept of Irrational Numbers
Is there an error in this question or solution?