Question

question
express in simplest radical form.
\\(\dfrac{\sqrt{48}}{8}\\)

Explanation:

Step1: Factor the radicand

Factor 48 into a product of a perfect square and another number. We know that \(48 = 16\times3\), where 16 is a perfect square. So, \(\sqrt{48}=\sqrt{16\times3}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we can rewrite \(\sqrt{16\times3}\) as \(\sqrt{16}\times\sqrt{3}\). Since \(\sqrt{16} = 4\), this becomes \(4\sqrt{3}\).

Step3: Substitute back and simplify the fraction

Now, substitute \(\sqrt{48}=4\sqrt{3}\) back into the original expression \(\frac{\sqrt{48}}{8}\). So we have \(\frac{4\sqrt{3}}{8}\).

Step4: Simplify the fraction

Simplify \(\frac{4\sqrt{3}}{8}\) by dividing the numerator and the denominator by their greatest common divisor, which is 4. \(\frac{4\div4\times\sqrt{3}}{8\div4}=\frac{\sqrt{3}}{2}\).

Answer:

\(\frac{\sqrt{3}}{2}\)