Question
(square root 11 + 9square root 3)squared
Answers
GPT-4o mini
To square the expression \((\sqrt{11} + 9\sqrt{3})\), we can use the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = \sqrt{11}\) and \(b = 9\sqrt{3}\).
Now, we can calculate each part:
1. \(a^2 = (\sqrt{11})^2 = 11\)
2. \(b^2 = (9\sqrt{3})^2 = 81 \cdot 3 = 243\)
3. \(2ab = 2 \cdot \sqrt{11} \cdot 9\sqrt{3} = 18\sqrt{33}\)
Now, we can put it all together:
\[
(\sqrt{11} + 9\sqrt{3})^2 = a^2 + 2ab + b^2 = 11 + 18\sqrt{33} + 243
\]
Adding \(11\) and \(243\):
\[
11 + 243 = 254
\]
Thus, the final result is:
\[
(\sqrt{11} + 9\sqrt{3})^2 = 254 + 18\sqrt{33}
\]
Now, we can calculate each part:
1. \(a^2 = (\sqrt{11})^2 = 11\)
2. \(b^2 = (9\sqrt{3})^2 = 81 \cdot 3 = 243\)
3. \(2ab = 2 \cdot \sqrt{11} \cdot 9\sqrt{3} = 18\sqrt{33}\)
Now, we can put it all together:
\[
(\sqrt{11} + 9\sqrt{3})^2 = a^2 + 2ab + b^2 = 11 + 18\sqrt{33} + 243
\]
Adding \(11\) and \(243\):
\[
11 + 243 = 254
\]
Thus, the final result is:
\[
(\sqrt{11} + 9\sqrt{3})^2 = 254 + 18\sqrt{33}
\]