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Simplify the term (3)/(sqrt(3)).

Mathematics

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Answer

1

Step-by-step solution

5 steps
  1. Simplify the term 33\frac{3}{\sqrt{3}}.

    To rationalize the denominator, multiply the numerator and denominator by 3\sqrt{3}.

    33=3×33×3=333=3\frac{3}{\sqrt{3}} = \frac{3 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{3\sqrt{3}}{3} = \sqrt{3}
  2. Substitute the simplified term back into the original expression.

    The expression becomes:

    3(3−233)\sqrt{3} \left( \sqrt{3} - \frac{2\sqrt{3}}{3} \right)
  3. Distribute 3\sqrt{3} into the terms inside the parenthesis.

    (3×3)−(3×233)\left( \sqrt{3} \times \sqrt{3} \right) - \left( \sqrt{3} \times \frac{2\sqrt{3}}{3} \right)
  4. Calculate each term.

    For the first term:

    3×3=3\sqrt{3} \times \sqrt{3} = 3

    For the second term:

    3×233=2×(3×3)3=2×33=63=2\sqrt{3} \times \frac{2\sqrt{3}}{3} = \frac{2 \times (\sqrt{3} \times \sqrt{3})}{3} = \frac{2 \times 3}{3} = \frac{6}{3} = 2
  5. Subtract the second term from the first term.

    3−2=13 - 2 = 1

    The final answer is 1.

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