Question

What is
$\sqrt{2} + \sqrt{3} + \sqrt{5}$
​

Answer 1

Q) √2 + √3 + √5

= 5.38233234744 Ans

Answer 2

Suppose 2–√+3–√=r is rational. Then

2=(r−3–√)2=r2−23–√+3

is rational, so that

3–√=r2+12r

is rational, a contradiction. □

Let ψ=2–√+3–√. Then, considering ϕ,

5=(ϕ−ψ)2=ϕ2−ψϕ+5+26–√.