The zeroes α and β of $x^2-20x+64$ are both positive. What is the value of √α + √β?

Square the expression first: $(\sqrt{\alpha }+\sqrt{\beta }{)}^2=\alpha +\beta +2\sqrt{\alpha \beta }=20+2\sqrt{64}=20+16=36$. Since both zeroes are positive, $\sqrt{\alpha }+\sqrt{\beta }=\sqrt{36}=6$. (Check with the zeroes 16 and 4: $4+2=6$.) 36 forgets the final square root; 20 uses only $\alpha +\beta$; $\sqrt{20}$ omits the $2\sqrt{\alpha \beta }$ cross term.