# What is the conjugate of the square root of 2 + the square root of 3 + the square root of 5?

$\sqrt{2} + \sqrt{3} + \sqrt{5}$ does not have one conjugate. If you are trying to eliminate it from a denominator, then you need to multiply by something like:
$\left(\sqrt{2} + \sqrt{3} - \sqrt{5}\right) \left(\sqrt{2} - \sqrt{3} + \sqrt{5}\right) \left(\sqrt{2} - \sqrt{3} - \sqrt{5}\right)$
The product of $\left(\sqrt{2} + \sqrt{3} + \sqrt{5}\right)$ and this is $- 24$