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Algebra help? Fast please! Simplifying radical expressions by rationalizing the denominator

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1 Answer

-10/(4-√3)
 
Multiply by the conjugate: (4+√3)/(4+√3)

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In my past things though, I would've had to multiply by the denominator.
like square root 5 over square root three would be square root 15 over 3

why does it have to be the opposite 
The goal of "rationalizing" a rational expression is to eliminate any roots (√) in the denominator.  If you have a monomial (one term) root in the denominator, such as:
 
√15/√3
 
Then you just multiply the expression by √3/√3 and you'll get √45/3 = 2√10/3, so you've eliminated the square root in the denominator.  If the denominator is a binomial - two terms added together - such as 4-√3, then you need to use the conjugate, 4+√3 to eliminate the radical in thel denominator:
 
(4-√3)(4+√3) = 42 + 4√3 - 4√3 - √3√3 = 16-3 = 13
 
No square root!
 
 

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