Question

multiply, and then simplify if possible.
\sqrt{10}(\sqrt{3} + \sqrt{7})

Explanation:

Step1: Apply distributive property

Using the distributive property \(a(b + c)=ab+ac\), where \(a = \sqrt{10}\), \(b=\sqrt{3}\), and \(c = \sqrt{7}\), we get:
\(\sqrt{10}\times\sqrt{3}+\sqrt{10}\times\sqrt{7}\)

Step2: Multiply square roots

Recall that \(\sqrt{m}\times\sqrt{n}=\sqrt{mn}\) for non - negative real numbers \(m\) and \(n\).
For \(\sqrt{10}\times\sqrt{3}\), we have \(\sqrt{10\times3}=\sqrt{30}\).
For \(\sqrt{10}\times\sqrt{7}\), we have \(\sqrt{10\times7}=\sqrt{70}\).

Answer:

\(\sqrt{30}+\sqrt{70}\)