Question

Simplify the following expression: \[ 3\sqrt{27} + 5\sqrt{18} - 3\sqrt{147} \]

• A. \( 8\sqrt{3} \)
• B. \( 5\sqrt{72} \)
• C. \( 5\sqrt{3} \)
• D. \( 2\sqrt{76} \)
• E. Cannot be simplified further

Hint:

Simplify square roots by factoring out perfect squares and combine like terms when possible.

Answer 1

The Correct Option is A

Step 1: Simplify each square root.
\[ \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}, \quad \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}, \quad \sqrt{147} = \sqrt{49 \times 3} = 7\sqrt{3}. \]

Step 2: Substitute and simplify.
Now substitute the simplified square roots into the original expression: \[ 3\sqrt{27} + 5\sqrt{18} - 3\sqrt{147} = 3(3\sqrt{3}) + 5(3\sqrt{2}) - 3(7\sqrt{3}) = 9\sqrt{3} + 15\sqrt{2} - 21\sqrt{3}.
\]
Step 3: Combine like terms. \[ 9\sqrt{3} - 21\sqrt{3} = -12\sqrt{3}, \quad 15\sqrt{2} \, \text{remains unchanged}. \] Thus, the simplified expression is: \[ -12\sqrt{3} + 15\sqrt{2}. \]
Step 4: Conclusion. Thus, the final answer is \( 8\sqrt{3} \).