Simplify sqrt(50) + sqrt(18)

Answer

\boxed{8\sqrt{2}}

Checking by squaring both sides: $(8\sqrt{2})^2 = 64 \cdot 2 = 128$ , and $(\sqrt{50} + \sqrt{18})^2 = 50 + 2\sqrt{900} + 18 = 68 + 2(30) = 128$ , which matches.

Problem: Simplify $\sqrt{50} + \sqrt{18}$

Steps

Factor radicals $\sqrt{25 \cdot 2} + \sqrt{9 \cdot 2}$
Apply the product rule for radicals $\sqrt{25}\sqrt{2} + \sqrt{9}\sqrt{2}$
Simplify perfect squares $5\sqrt{2} + 3\sqrt{2}$
Combine like terms $8\sqrt{2}$

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