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Bentuk sederhana dari 5sqrt(243)+2sqrt(27)-sqrt(75)-3sqrt(48) adalah ...

Mathematics

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Answer

A. 343\text{A. } 34\sqrt{3}

Step-by-step solution

3 steps

To simplify the expression, we need to simplify each square root term by factoring out perfect squares.

  1. Simplify each term.

    5243=581×3=5×93=4535\sqrt{243} = 5\sqrt{81 \times 3} = 5 \times 9\sqrt{3} = 45\sqrt{3} 227=29×3=2×33=632\sqrt{27} = 2\sqrt{9 \times 3} = 2 \times 3\sqrt{3} = 6\sqrt{3} 75=25×3=53\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3} 348=316×3=3×43=1233\sqrt{48} = 3\sqrt{16 \times 3} = 3 \times 4\sqrt{3} = 12\sqrt{3}
  2. Substitute the simplified terms back into the original expression.

    453+63−53−12345\sqrt{3} + 6\sqrt{3} - 5\sqrt{3} - 12\sqrt{3}
  3. Combine the coefficients of 3\sqrt{3}.

    (45+6−5−12)3(45 + 6 - 5 - 12)\sqrt{3} (51−5−12)3(51 - 5 - 12)\sqrt{3} (46−12)3(46 - 12)\sqrt{3} 34334\sqrt{3}

    The simplified form is 34334\sqrt{3}. Comparing this with the given options, it matches option A.

    The final answer is A. 343\text{A. } 34\sqrt{3}.

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