Rationalizing Denominators Math Example 1

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Example 1

easy
Rationalize the denominator of 53\frac{5}{\sqrt{3}}.

Solution

  1. 1
    Step 1: Multiply numerator and denominator by 3\sqrt{3}.
  2. 2
    Step 2: 53⋅33=533\frac{5}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{5\sqrt{3}}{3}.
  3. 3
    Check: 53≈51.732≈2.887\frac{5}{\sqrt{3}} \approx \frac{5}{1.732} \approx 2.887 and 5(1.732)3≈2.887\frac{5(1.732)}{3} \approx 2.887 ✓

Answer

533\frac{5\sqrt{3}}{3}
Rationalizing means removing radicals from the denominator. Multiply top and bottom by the radical in the denominator — this creates a perfect square in the denominator.

About Rationalizing Denominators

The process of eliminating radical expressions from the denominator of a fraction by multiplying the numerator and denominator by an appropriate expression (the radical itself or its conjugate).

Learn more about Rationalizing Denominators →

More Rationalizing Denominators Examples

Example 2 hard

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Example 4 medium

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