  # Rationalize a 3 term Denominator

by Asia
(Las Vegas) Rationalize a 3 term Denominator

Rationalize a Denominator containing 3 terms

The difference of squares formula states that:

(a + b)(a − b) = a^2 − b^2

You can apply the same reasoning to rationalize a denominator which contains three terms by grouping the terms.

Rationalize the denominator of the following expression.

1/(1+3^1/2-5^1/2)

### Comments for Rationalize a 3 term Denominator

 Feb 15, 2011 Rationalize a 3 term Denominator by: Staff The question: by Asia (Las Vegas)1/(1+3^1/2-5^1/2)The answer:Your problem has three terms in the denominator: a + b + cHowever, imagine for a moment how you would rationalize a denominator with only two terms: a + b.As you know, if the denominator contains only two terms, you could rationalize the denominator by multiplying the denominator by its conjugate: a - b. The difference of squares formula states that:(a + b)(a − b) = a^2 − b^2You can apply the same reasoning to rationalize a denominator which contains three terms. GROUP THE TERMS as follows:a + b + c = (a + b) + cThe difference of squares formula states that:[(a + b) + c] * [(a + b) - c] = (a + b) ^2 − c^2Original Problem:1/(1+3^1/2-5^1/2)Group the denominator so that the difference of squares formula can be applied:1/[(1 + 3^1/2) - 5^1/2]Multiply by the conjugate: [(1 + 3^1/2) + 5^1/2]1/[(1 + 3^1/2) - 5^1/2]{1/[(1 + 3^1/2) - 5^1/2]} * {[(1 + 3^1/2) + 5^1/2] / [(1 + 3^1/2) + 5^1/2]}(1 + 3^1/2 + 5^1/2) / [(1 + 3^1/2)^2 + (5^1/2)^2](1 + 3^1/2 + 5^1/2) / (1 + 2*3^1/2 +3 ? 5)(1 + 3^1/2 + 5^1/2) / (2*3^1/2 ? 1)Repeat the process - Multiply by the new conjugate: (2*3^1/2 + 1)(1 + 3^1/2 + 5^1/2) / (2*3^1/2 ? 1)[(1 + 3^1/2 + 5^1/2) / (2*3^1/2 ? 1)] * [(2*3^1/2 + 1)/ (2*3^1/2 + 1)][(1 + 3^1/2 + 5^1/2) * (2*3^1/2 + 1)] / [(2*3^1/2 ? 1) * (2*3^1/2 + 1)][(1 + 3^1/2 + 5^1/2) * (2*3^1/2 + 1)] / (2*3^1/2)^2 ? 1^2)[(1 + 3^1/2 + 5^1/2) * (2*3^1/2 + 1)] / (12 - 1)[(1 + 3^1/2 + 5^1/2) * (2*3^1/2 + 1)] / 11(2 * 3^1/2 + 6 + 2 * 15^1/2 + 1 + 3^1/2 + 5^1/2) / 11(7 + 3 * 3^1/2 + 5^1/2 + 2 * 15^1/2) / 11The final answer is: (7 + 3 * 3^1/2 + 5^1/2 + 2 * 15^1/2) / 11Thanks for writing.Staff www.solving-math-problems.com

 Sep 06, 2016 rationalixe the denominator NEW by: Anonymous i ask rationalize the denominaor with three terms and diffrents coeffients

 Jun 03, 2017 Plz tell how to solve the given ques NEW by: Anonymous √3-√4 upon √3+√4-√7