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