Rationalizing Denominators Math Example 4

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Example 4

medium
Rationalize 62−1\frac{6}{\sqrt{2} - 1}.

Solution

  1. 1
    Multiply by conjugate: 6(2+1)(2)2−12=6(2+1)2−1=6(2+1)\frac{6(\sqrt{2} + 1)}{(\sqrt{2})^2 - 1^2} = \frac{6(\sqrt{2} + 1)}{2 - 1} = 6(\sqrt{2} + 1).
  2. 2
    =62+6= 6\sqrt{2} + 6.

Answer

62+66\sqrt{2} + 6
Using the conjugate 2+1\sqrt{2} + 1 eliminates the radical from the denominator. Here the denominator simplifies to 1, making the result especially clean.

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).

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More Rationalizing Denominators Examples

Example 1 easy

Rationalize the denominator of [formula].

Example 2 hard

Rationalize [formula].

Example 3 easy

Rationalize [formula].

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