QuestionAugust 26, 2025

19) 3sqrt (18)+3sqrt (12)+2sqrt (27)

19) 3sqrt (18)+3sqrt (12)+2sqrt (27)
19) 3sqrt (18)+3sqrt (12)+2sqrt (27)

Solution
4.1(235 votes)

Answer

9\sqrt{2} + 12\sqrt{3} Explanation 1. Simplify each square root \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}, \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}, \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}. 2. Substitute simplified roots back into the expression 3\sqrt{18} = 3 \times 3\sqrt{2} = 9\sqrt{2}, 3\sqrt{12} = 3 \times 2\sqrt{3} = 6\sqrt{3}, 2\sqrt{27} = 2 \times 3\sqrt{3} = 6\sqrt{3}. 3. Combine like terms 9\sqrt{2} + 6\sqrt{3} + 6\sqrt{3} = 9\sqrt{2} + 12\sqrt{3}.

Explanation

1. Simplify each square root<br /> $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$, $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$, $\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$.<br /><br />2. Substitute simplified roots back into the expression<br /> $3\sqrt{18} = 3 \times 3\sqrt{2} = 9\sqrt{2}$, $3\sqrt{12} = 3 \times 2\sqrt{3} = 6\sqrt{3}$, $2\sqrt{27} = 2 \times 3\sqrt{3} = 6\sqrt{3}$.<br /><br />3. Combine like terms<br /> $9\sqrt{2} + 6\sqrt{3} + 6\sqrt{3} = 9\sqrt{2} + 12\sqrt{3}$.
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