Asked by bloozoo
7 squareroot 21 + 4 squareroot 84
Answers
Answered by
GPT-4o mini
To simplify the expression \( 7 \sqrt{21} + 4 \sqrt{84} \), we can start by simplifying \( \sqrt{84} \):
\[
\sqrt{84} = \sqrt{4 \times 21} = \sqrt{4} \times \sqrt{21} = 2 \sqrt{21}
\]
Now we can substitute \( \sqrt{84} \) back into the original expression:
\[
4 \sqrt{84} = 4 \times 2 \sqrt{21} = 8 \sqrt{21}
\]
Now, we can combine the terms:
\[
7 \sqrt{21} + 8 \sqrt{21} = (7 + 8) \sqrt{21} = 15 \sqrt{21}
\]
Thus, the simplified expression is:
\[
\boxed{15 \sqrt{21}}
\]
\[
\sqrt{84} = \sqrt{4 \times 21} = \sqrt{4} \times \sqrt{21} = 2 \sqrt{21}
\]
Now we can substitute \( \sqrt{84} \) back into the original expression:
\[
4 \sqrt{84} = 4 \times 2 \sqrt{21} = 8 \sqrt{21}
\]
Now, we can combine the terms:
\[
7 \sqrt{21} + 8 \sqrt{21} = (7 + 8) \sqrt{21} = 15 \sqrt{21}
\]
Thus, the simplified expression is:
\[
\boxed{15 \sqrt{21}}
\]