Question

simplify. assume that all variables represent positive real numbers.\\(\sqrt{128} - 5\sqrt{32} + 7\sqrt{8}\\)\\(\circ -8\sqrt{2}\\)\\(\circ 42\sqrt{2}\\)\\(\circ \sqrt{2}\\)\\(\circ 2\sqrt{2}\\)

Explanation:

Step1: Simplify each square root

Simplify \(\sqrt{128}\), \(\sqrt{32}\), and \(\sqrt{8}\) by factoring out perfect squares.

• \(\sqrt{128} = \sqrt{64\times2} = \sqrt{64}\times\sqrt{2} = 8\sqrt{2}\)
• \(5\sqrt{32} = 5\sqrt{16\times2} = 5\times\sqrt{16}\times\sqrt{2} = 5\times4\sqrt{2} = 20\sqrt{2}\)
• \(7\sqrt{8} = 7\sqrt{4\times2} = 7\times\sqrt{4}\times\sqrt{2} = 7\times2\sqrt{2} = 14\sqrt{2}\)

Step2: Substitute and simplify the expression

Substitute the simplified square roots back into the original expression:

$$
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$$

Answer:

\(2\sqrt{2}\)