Question

simplify the following radical expression.\\(sqrt{48}\\)

Explanation:

Step1: Factor 48 into prime factors

We know that \(48 = 16\times3\), where 16 is a perfect square.

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

So, \(\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}\)

Step3: Simplify \(\sqrt{16}\)

Since \(4^2 = 16\), then \(\sqrt{16}=4\)

Step4: Combine the results

We get \(4\times\sqrt{3}=4\sqrt{3}\)

Answer:

\(4\sqrt{3}\)