Question

Multiply. Write your answer in simplest form.

10 squareroot7 (6 squareroot91 + squareroot2)

Answer 1

To multiply the expression \(10 \sqrt{7} (6 \sqrt{91} + \sqrt{2})\), we will use the distributive property (also known as the FOIL method).

1. Distribute \(10 \sqrt{7}\) to each term inside the parentheses:
\[
10 \sqrt{7} \cdot 6 \sqrt{91} + 10 \sqrt{7} \cdot \sqrt{2}
\]

2. Calculate each part separately.

For the first term:
\[
10 \sqrt{7} \cdot 6 \sqrt{91} = 60 \sqrt{7} \cdot \sqrt{91}
\]

Recall that \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). Thus,
\[
60 \sqrt{7 \cdot 91} = 60 \sqrt{637}
\]

Next, for the second term:
\[
10 \sqrt{7} \cdot \sqrt{2} = 10 \sqrt{7 \cdot 2} = 10 \sqrt{14}
\]

3. Combine the two results:
\[
60 \sqrt{637} + 10 \sqrt{14}
\]

Thus, the final answer in simplest form is:
\[
\boxed{60 \sqrt{637} + 10 \sqrt{14}}
\]