Question
square root 14 (-2 - 10square root 91)
Answers
GPT-4o mini
To simplify the expression \(\sqrt{14} (-2 - 10\sqrt{91})\), we can distribute \(\sqrt{14}\) through the terms inside the parentheses.
Starting with:
\[
\sqrt{14} (-2 - 10\sqrt{91})
\]
This can be rewritten as:
\[
\sqrt{14} \cdot (-2) + \sqrt{14} \cdot (-10\sqrt{91})
\]
Calculating each term:
1. The first term is:
\[
-2\sqrt{14}
\]
2. The second term is:
\[
-10\sqrt{14} \cdot \sqrt{91} = -10\sqrt{14 \cdot 91}
\]
Now, we can multiply \(14\) and \(91\):
\[
14 \cdot 91 = 1274
\]
So the second term can be expressed as:
\[
-10\sqrt{1274}
\]
Putting it all together, we have:
\[
-2\sqrt{14} - 10\sqrt{1274}
\]
Thus, the simplified form of the expression \(\sqrt{14} (-2 - 10\sqrt{91})\) is:
\[
-2\sqrt{14} - 10\sqrt{1274}
\]
If you need a numerical approximation or further simplification of \(\sqrt{1274}\), it approximately equals \(35.7\), but typically it is left in radical form unless specified otherwise.
Starting with:
\[
\sqrt{14} (-2 - 10\sqrt{91})
\]
This can be rewritten as:
\[
\sqrt{14} \cdot (-2) + \sqrt{14} \cdot (-10\sqrt{91})
\]
Calculating each term:
1. The first term is:
\[
-2\sqrt{14}
\]
2. The second term is:
\[
-10\sqrt{14} \cdot \sqrt{91} = -10\sqrt{14 \cdot 91}
\]
Now, we can multiply \(14\) and \(91\):
\[
14 \cdot 91 = 1274
\]
So the second term can be expressed as:
\[
-10\sqrt{1274}
\]
Putting it all together, we have:
\[
-2\sqrt{14} - 10\sqrt{1274}
\]
Thus, the simplified form of the expression \(\sqrt{14} (-2 - 10\sqrt{91})\) is:
\[
-2\sqrt{14} - 10\sqrt{1274}
\]
If you need a numerical approximation or further simplification of \(\sqrt{1274}\), it approximately equals \(35.7\), but typically it is left in radical form unless specified otherwise.