Question

simplify
\\( \sqrt{7}(\sqrt{3} + 7) \\)
\\( \bigcirc \\) a \\( \sqrt{10} + 7 \\)
\\( \bigcirc \\) b \\( \sqrt{10} + 7\sqrt{7} \\)
\\( \bigcirc \\) c \\( \sqrt{21} + 7 \\)
\\( \bigcirc \\) d \\( \sqrt{21} + 7\sqrt{7} \\)

Explanation:

Step1: Apply distributive property

Using the distributive property \(a(b + c)=ab+ac\), where \(a = \sqrt{7}\), \(b=\sqrt{3}\), and \(c = 7\), we get:
\(\sqrt{7}\times\sqrt{3}+\sqrt{7}\times7\)

Step2: Simplify square root multiplication

Recall that \(\sqrt{m}\times\sqrt{n}=\sqrt{mn}\) for non - negative real numbers \(m\) and \(n\). So \(\sqrt{7}\times\sqrt{3}=\sqrt{7\times3}=\sqrt{21}\), and \(\sqrt{7}\times7 = 7\sqrt{7}\).
Combining these results, we have \(\sqrt{21}+7\sqrt{7}\).

Answer:

D. \(\boldsymbol{\sqrt{21}+7\sqrt{7}}\)