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Question

Rationalize the denominator: How do I solve this step by step?
5____
√[6] + √[5]

Answer 1

5 / √∣6∣+ √∣5∣=

5 / √6 + √5 =

5(√6 - √5) / ( √6 + √5 )(√6 - √5) =

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Working the denominator

FOIL

(√6 + √5)(√6 - √5 =

√6√6 + √6√5 - √6√5 - √5√5 =

√36 - √25 =

6 - 5 =

1

Insert the 1 into the denominator

5(√6 - √5) / 1 =

5√6 - 5√5 / 1

- - - - - - - s-

Answer 2

Multiply numerator and denominator by sqrt(6) - sqrt(5).
That gives:
5[ sqrt(6) - sqrt(5) ] / [ sqrt(6) + sqrt(5) ][sqrt(6) - sqrt(5) ]
The denominator now multiplies out to the difference of two squares: [ sqrt(6) ]^2 - [ sqrt(5) ]^2 = 6 - 5 = 1.
That makes the whole expression 5[ sqrt(6) - sqrt(5) ] / 1, and since the denominator 1 is redundant, the result is:
5[ sqrt(6) - sqrt(5) ] .

Answer 3

5____
(√6 + √5)

= 5(√6 - √5)______
(√6 + √5)(√6 - √5)

= 5(√6 - √5)/(6 - 5)

= 5(√6 - √5)/1

= 5√6 - 5√5

Answer 4

You multiply top and bottom by √[6] - √[5].

It will become

5(√[6] - √[5]) / (√[6] + √[5])(√[6] - √[5])

= 5(√[6] - √[5])/1

Answer 5

the denominator is of the form sqrt(6)+ sqrt(5)

multiply both numerator and denominator by sqrt(6)-sqrt(5)

numerator = 5(sqrt(6)- sqrt(5))
denominator = (sqrt(6)+sqrt(5))(sqrt(6)- sqrt(5))
= (sqrt(6))^2-(sqrt(5))^2 = 6- 5
= 1
so fraction = 5(sqrt(6)- sqrt(5))