Question

simplify
\\(\sqrt{448} + \sqrt{63}\\)
\\(\circ\\) \\(5\sqrt{11}\\)
\\(\circ\\) \\(11\sqrt{7}\\)
\\(\circ\\) \\(24\sqrt{7}\\)
\\(\circ\\) \\(\sqrt{511}\\)

Explanation:

Step1: Simplify $\sqrt{448}$

Factor 448 to find perfect square factors. $448 = 64\times7$, and $\sqrt{64\times7}=\sqrt{64}\times\sqrt{7}=8\sqrt{7}$.

Step2: Simplify $\sqrt{63}$

Factor 63 to find perfect square factors. $63 = 9\times7$, and $\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}=3\sqrt{7}$.

Step3: Add the simplified radicals

Now add $8\sqrt{7}$ and $3\sqrt{7}$. Since they are like radicals, we add the coefficients: $8\sqrt{7}+3\sqrt{7}=(8 + 3)\sqrt{7}=11\sqrt{7}$.

Answer:

$11\sqrt{7}$ (corresponding to the option "11√7")