Verified answer

2/(√[6] – √[5])

To rationalize this, multiply the top and bottom by the conjugate of the bottom. The conjugate of (√[6] – √[5]) is

(√[6] + √[5]).

2(√[6] + √[5]) / [ (√[6] – √[5]) (√[6] + √[5]) ]

Remember that conjugates multiply out as a difference of squares; that is, (a - b)(a + b) = a^2 - b^2. In the case of radicals (square roots), that just eliminates the square roots, and we get

2(√[6] + √[5]) / [ 6 - 5 ]

Simplifying,

2(√[6] + √[5]) / 1

2(√[6] + √[5])

Voila; rationalized.

2/√[6] – √[5]?

Multiply numeratos and denominator by √[6] + √[5] to obtain

2 (√[6] + √[5]) /([6] – [5]) = 2(√[6] + √[5])

multiply numerator and denominator by sqrt6+sqrt5

in num you will have: 2(sqrt6+sqrt5)

in den you will have: 6-5=1

therefore your answer: 2((sqrt6+sqrt5))/1=2(sqrt6+sqrt5)

here we used difference of 2 squares:

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

(sqrt of a)*(sqrt of a)=(sqrt of a)^2=a if a>=0

2/(sq.rt6-sq.rt5)

=2/(sq.rt6-sq.rt5)*(sq.rt6+sq.rt5)/(sq.rt6+sq.rt5)

=2(sq.rt6+sq.rt5)/((sq.rt6)^2-(sq.rt5)^2)

=2(sq.rt6+sq.rt5)/(6-5)

=2(sq.rt6+sq.rt5)/1

=2(sq.rt6+sq.rt5)