Question
Subtract. Write your answer in simplest form.
–6√21 – 2√84
–6√21 – 2√84
Answers
GPT-4o mini
To simplify the expression \(-6\sqrt{21} - 2\sqrt{84}\), we first simplify \(\sqrt{84}\).
1. Find the prime factorization of 84:
\[
84 = 2^2 \times 3 \times 7
\]
2. Now, take the square root of each factor:
\[
\sqrt{84} = \sqrt{2^2 \times 3 \times 7} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{7} = 2\sqrt{21}
\]
3. Substitute \(\sqrt{84}\) back into the expression:
\[
-6\sqrt{21} - 2\sqrt{84} = -6\sqrt{21} - 2(2\sqrt{21}) = -6\sqrt{21} - 4\sqrt{21}
\]
4. Now, combine the like terms:
\[
-6\sqrt{21} - 4\sqrt{21} = (-6 - 4)\sqrt{21} = -10\sqrt{21}
\]
Thus, the final answer is:
\[
\boxed{-10\sqrt{21}}
\]
1. Find the prime factorization of 84:
\[
84 = 2^2 \times 3 \times 7
\]
2. Now, take the square root of each factor:
\[
\sqrt{84} = \sqrt{2^2 \times 3 \times 7} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{7} = 2\sqrt{21}
\]
3. Substitute \(\sqrt{84}\) back into the expression:
\[
-6\sqrt{21} - 2\sqrt{84} = -6\sqrt{21} - 2(2\sqrt{21}) = -6\sqrt{21} - 4\sqrt{21}
\]
4. Now, combine the like terms:
\[
-6\sqrt{21} - 4\sqrt{21} = (-6 - 4)\sqrt{21} = -10\sqrt{21}
\]
Thus, the final answer is:
\[
\boxed{-10\sqrt{21}}
\]