Question

8square root 2(9 + 5square root 22)

Answer 1

To simplify the expression \( 8\sqrt{2}(9 + 5\sqrt{22}) \), you'll want to distribute \( 8\sqrt{2} \) to both terms inside the parentheses.

Starting with the expression:

\[
8\sqrt{2}(9 + 5\sqrt{22})
\]

Distributing \( 8\sqrt{2} \):

\[
= 8\sqrt{2} \cdot 9 + 8\sqrt{2} \cdot 5\sqrt{22}
\]

Calculating each term:

1. The first term:
\[
8\sqrt{2} \cdot 9 = 72\sqrt{2}
\]

2. The second term:
\[
8\sqrt{2} \cdot 5\sqrt{22} = 40\sqrt{2 \cdot 22} = 40\sqrt{44}
\]
Since \( \sqrt{44} = \sqrt{4 \cdot 11} = 2\sqrt{11} \):
\[
40\sqrt{44} = 40 \cdot 2\sqrt{11} = 80\sqrt{11}
\]

Now combine the results:

\[
72\sqrt{2} + 80\sqrt{11}
\]

Thus, the simplified expression is:

\[
72\sqrt{2} + 80\sqrt{11}
\]