Question

Which one is greater? √5 + √3 or √6 + √2

Answer 1

Hi,

the greater is

`√(5) +√(3)`

Explanation:

`12 < 15\\\\\Longrightarrow\ √(12) < √(15) \\\\\Longrightarrow\ 2√(12) < 2√(15) \\\\\Longrightarrow\ 8+2√(12) < 8+2√(15) \\\\\Longrightarrow\ 6+2+2√(12) < 5+3+2√(15) \\\\\Longrightarrow\ (√(6)+√(2))^2 < (√(5)+√(3))^2 \\\\\Longrightarrow\ \boxed{√(6)+√(2) < √(5)+√(3)} \\`

Answer 2

Answer:


`image`


`image`

So the first is bigger (
`√(5) + √(3)`)