simplifying nonperfect roots\nwhich expression is equivalent to \\(\\sqrt{120x}\\)?\n\\(2\\sqrt{30}\\)…
simplifying nonperfect roots\nwhich expression is equivalent to \\(\\sqrt{120x}\\)?\n\\(2\\sqrt{30}\\) \\(2\\sqrt{30x}\\) \\(4\\sqrt{30x}\\)\n\\(60\\sqrt{2x}\\)
Answer
Explanation:
Step1: Factor the radicand
Factor 120 into its prime factors: (120 = 4\times30), so (\sqrt{120x}=\sqrt{4\times30x}).
Step2: Use the square - root property (\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}) ((a\geq0,b\geq0))
We know that (\sqrt{4\times30x}=\sqrt{4}\times\sqrt{30x}). Since (\sqrt{4} = 2), then (\sqrt{4}\times\sqrt{30x}=2\sqrt{30x}).