Simplify each radical expression. leave in radical form. show your work.√ (17+2√22)

First put the equation under one denominator.
17/1+2/√22 = (17√22 + 2)/√22
rationalize this equation by multiplying both numerator and denominator by √22.

= (17×√22×√22 + 2×√22)/(√22×√22)
= (17×22 +2√22)/22
= (374 +2√22)/22

So, from the equation, 
√ (17+2√22) = √((374 + 2√22)/22)