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How can you write the expression with a rationalized denominator? √3-√6 divided...

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connorcolin3 | Valedictorian

Posted December 26, 2012 at 9:54 PM via web

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How can you write the expression with a rationalized denominator?

√3-√6 divided by √3+√6

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jgeertz | College Teacher | (Level 1) Associate Educator

Posted December 27, 2012 at 12:58 AM (Answer #1)

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`(sqrt3 -sqrt6)/(sqrt3+sqrt6)`

To rationalize the denominator of a fraction, rewrite the fraction so the new fraction has the same value as the original but with a rational denominator.

`(sqrt3-sqrt6)/(sqrt3+sqrt6)*(sqrt3-sqrt6)/(sqrt3-sqrt6)`

Now use the difference of squares formula to factor.

`a^2-b^2 =(a-b)(a+b)`

`((sqrt3-sqrt6)*(sqrt3-sqrt6))/((sqrt3)^2-(sqrt6)^2)`

Square each of the expressions in the denominator.

`((sqrt3-sqrt6)(sqrt3-sqrt6))/(3-(6))`

Simplify the rationalized expression.

The solution is:

`-3+2sqrt2`

 

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