Question

Simplify square root of five times the quantity eight plus three square root of six.

a eight square root of five end root plus three square root of thirty
b five square root of ten
c 130
d square root of 40 end root plus 15 square root of 6

Answer 1

Let's simplify the expression \(\sqrt{5} \times (8 + 3\sqrt{6})\).

We can distribute \(\sqrt{5}\) across the terms in the parentheses:

\[
\sqrt{5} \times (8 + 3\sqrt{6}) = \sqrt{5} \times 8 + \sqrt{5} \times 3\sqrt{6}
\]

This simplifies to:

\[
8\sqrt{5} + 3\sqrt{5} \cdot \sqrt{6}
\]

Now, we can simplify \(3\sqrt{5} \cdot \sqrt{6}\) using the property that \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\):

\[
3\sqrt{5} \cdot \sqrt{6} = 3\sqrt{30}
\]

Therefore, the expression simplifies to:

\[
8\sqrt{5} + 3\sqrt{30}
\]

Now, looking at the answer choices provided:

a. \(8\sqrt{5} + 3\sqrt{30}\)
b. \(5\sqrt{10}\)
c. 130
d. \(\sqrt{40} + 15\sqrt{6}\)

The simplified result \(8\sqrt{5} + 3\sqrt{30}\) matches with option **a**.

So, the correct answer is:

**a \(8\sqrt{5} + 3\sqrt{30}\)**.