Question
5 squareroot 48 + 9 squareroot 3, what is this simplified?
Answers
GPT-4o mini
To simplify the expression \( 5\sqrt{48} + 9\sqrt{3} \), we start by simplifying \( \sqrt{48} \).
1. **Simplifying \( \sqrt{48} \)**:
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]
2. **Substituting back into the expression**:
\[
5\sqrt{48} = 5(4\sqrt{3}) = 20\sqrt{3}
\]
3. **Now replace \( 5\sqrt{48} \) in the original expression**:
\[
20\sqrt{3} + 9\sqrt{3}
\]
4. **Combining like terms**:
\[
(20 + 9)\sqrt{3} = 29\sqrt{3}
\]
Thus, the simplified form of \( 5\sqrt{48} + 9\sqrt{3} \) is \( \boxed{29\sqrt{3}} \).
1. **Simplifying \( \sqrt{48} \)**:
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]
2. **Substituting back into the expression**:
\[
5\sqrt{48} = 5(4\sqrt{3}) = 20\sqrt{3}
\]
3. **Now replace \( 5\sqrt{48} \) in the original expression**:
\[
20\sqrt{3} + 9\sqrt{3}
\]
4. **Combining like terms**:
\[
(20 + 9)\sqrt{3} = 29\sqrt{3}
\]
Thus, the simplified form of \( 5\sqrt{48} + 9\sqrt{3} \) is \( \boxed{29\sqrt{3}} \).