Question

question
express in simplest radical form.
\sqrt{128}

Explanation:

Step1: Factor 128 into perfect square and other factor

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 the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

Applying the property, we get \(\sqrt{64\times2}=\sqrt{64}\times\sqrt{2}\).

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

Since \(8^2 = 64\), \(\sqrt{64}=8\). So the expression becomes \(8\sqrt{2}\).

Answer:

\(8\sqrt{2}\)