How do you rationalize the denominator and simplify 5√3+√5?

1 Answer
Don't Memorise
Oct 5, 2015

=−5(√3−√5)2

Explanation:

Rationalizing involves multiplying the numerator and the denominator of the expression by the conjugate of the denominator.

The conjugate of the denominator is
√3+√5=√3−√5

Rationalizing

5√3+√5=5⋅(√3−√5)(√3+√5)⋅(√3−√5)

The denominator can be simplified by applying the property
(a+b)(a−b)=a2−b2

So,
(√3+√5)⋅(√3−√5)=3−5=−2

The expression then becomes:

5√3−5√5−2

=5(√3−√5)−2

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