Question

Multiply. Write your answer in simplest form.

(squareroot13 + 9 squareroot55) (5 squareroot2 + squareroot11)

Answer 1

To multiply the expressions \((\sqrt{13} + 9\sqrt{55})(5\sqrt{2} + \sqrt{11})\), we can apply the distributive property (also known as the FOIL method for binomials). This means we will multiply each term in the first binomial by each term in the second binomial.

1. **Multiply \(\sqrt{13}\) by \(5\sqrt{2}\)**:
\[
\sqrt{13} \cdot 5\sqrt{2} = 5\sqrt{26}
\]

2. **Multiply \(\sqrt{13}\) by \(\sqrt{11}\)**:
\[
\sqrt{13} \cdot \sqrt{11} = \sqrt{143}
\]

3. **Multiply \(9\sqrt{55}\) by \(5\sqrt{2}\)**:
\[
9\sqrt{55} \cdot 5\sqrt{2} = 45\sqrt{110}
\]

4. **Multiply \(9\sqrt{55}\) by \(\sqrt{11}\)**:
\[
9\sqrt{55} \cdot \sqrt{11} = 9\sqrt{605}
\]

Next, we combine all the results:

\[
5\sqrt{26} + \sqrt{143} + 45\sqrt{110} + 9\sqrt{605}
\]

Since none of the terms can be simplified further (they all have different radicands), the expression is already in its simplest form.

Thus, the final answer is:

\[
\boxed{5\sqrt{26} + \sqrt{143} + 45\sqrt{110} + 9\sqrt{605}}
\]