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How do you rationalize the denominator of (30)/(sqrt(3)) and express the answer in surd form?

Mathematics

ScanSolve AI Answer

Answer

10310\sqrt{3}

Step-by-step solution

4 steps

To leave the answer in surd form, we need to rationalize the denominator.

  1. Write the given expression.

    303\frac{30}{\sqrt{3}}

  2. Multiply the numerator and the denominator by 3\sqrt{3} to remove the radical from the denominator.

    303×33\frac{30}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}

  3. Perform the multiplication.

    30×33×3=3033\frac{30 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{30\sqrt{3}}{3}

  4. Simplify the fraction.

    3033=103\frac{30\sqrt{3}}{3} = 10\sqrt{3}

    The simplified expression in surd form is 10310\sqrt{3}.

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