Questions: Multiply. √2(√50-4) (Simplify your answer. Type an exact answer, using radicals as needed. Do not factor.)

Solution Steps

To solve the given expression, we need to distribute $\sqrt{2}$ to both terms inside the parentheses. This involves multiplying $\sqrt{2}$ by $\sqrt{50}$ and $\sqrt{2}$ by $-4$. We then simplify the resulting radicals.

We start with the expression: $$\sqrt{2}(\sqrt{50} - 4)$$ We distribute $\sqrt{2}$ to both $\sqrt{50}$ and $-4$: $$\sqrt{2} \cdot \sqrt{50} - \sqrt{2} \cdot 4$$

Next, we simplify the radicals: $$\sqrt{2} \cdot \sqrt{50} = \sqrt{2 \cdot 50} = \sqrt{100} = 10$$ $$\sqrt{2} \cdot 4 = 4\sqrt{2}$$

We combine the simplified terms: $$10 - 4\sqrt{2}$$

Final Answer