Question

simplifying square roots independent pract
started: jan 29 at 8:39am
quiz instructions
question 1 1 pts
what is \\(\sqrt{128}\\) written in simplest radical form?
\\(\circ\\) \\(4\sqrt{8}\\)
\\(\circ\\) \\(16\sqrt{8}\\)
\\(\circ\\) \\(8\sqrt{2}\\)
\\(\circ\\) \\(64\sqrt{2}\\)

Explanation:

Step1: Factor 128 into perfect square and other

We know that \(128 = 64\times2\), where \(64\) is a perfect square (\(8^2 = 64\)). So we can rewrite \(\sqrt{128}\) as \(\sqrt{64\times2}\).

Step2: Use square root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we have \(\sqrt{64\times2}=\sqrt{64}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{64}\)

Since \(\sqrt{64} = 8\), then \(\sqrt{64}\times\sqrt{2}=8\sqrt{2}\).

Answer:

\(8\sqrt{2}\) (corresponding to the option \(8\sqrt{2}\))