Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)
Question 1 Report
Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)
Answer Details
First, we simplify the term inside the square root in the numerator:
\begin{align*}
\sqrt{3} + \sqrt{48} &= \sqrt{3} + \sqrt{16\cdot3} \\
&= \sqrt{3} + \sqrt{16}\sqrt{3} \\
&= \sqrt{3} + 4\sqrt{3} \\
&= 5\sqrt{3}.
\end{align*}
Now we substitute this simplified value back into the original expression:
\begin{align*}
\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}} &= \frac{5\sqrt{3}}{\sqrt{6}} \\
&= \frac{5\sqrt{3}}{\sqrt{2}\sqrt{3}} \\
&= \frac{5}{\sqrt{2}} \\
&= \frac{5\sqrt{2}}{2}.
\end{align*}
Therefore, the simplified expression is \(\frac{5\sqrt{2}}{2}\).
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