Question
Simplify the radical expression. −5+20−512 Responses −5−103 negative square root of 5 minus 10 square root of 3 5−103 square root of 5 minus 10 square root of 3 35−103 3 square root of 5 minus 10 square root of 3
Answers
GPT-4o mini
To simplify the expression \(-5 + 20 - 5 \sqrt{12}\), we can follow these steps:
1. Combine the constant numbers:
\(-5 + 20 = 15\)
2. Simplify the square root term:
\(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\)
So, \(5 \sqrt{12} = 5 \times 2 \sqrt{3} = 10 \sqrt{3}\).
3. Now, substitute this back into the expression:
\[
15 - 10\sqrt{3}
\]
Thus, the simplified expression becomes:
\[
15 - 10\sqrt{3}
\]
Therefore, the right option for the simplified expression could be "15 - 10 square root of 3". If that option isn't listed, please provide the full list for clarification.
1. Combine the constant numbers:
\(-5 + 20 = 15\)
2. Simplify the square root term:
\(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\)
So, \(5 \sqrt{12} = 5 \times 2 \sqrt{3} = 10 \sqrt{3}\).
3. Now, substitute this back into the expression:
\[
15 - 10\sqrt{3}
\]
Thus, the simplified expression becomes:
\[
15 - 10\sqrt{3}
\]
Therefore, the right option for the simplified expression could be "15 - 10 square root of 3". If that option isn't listed, please provide the full list for clarification.