Respuesta :

musiclover10045

(5 - √2) / √3

Multiply the fraction by √3 / √3:

((5 - √2) * √3) / (√3 *√3)

Simplify to get (5√3 - √6) / 3

wegnerkolmp2741o

Answer:

1/3 (5sqrt(3) - sqrt(6))

Step-by-step explanation:

To rationalize the denominator, we need to get rid of the square root.

We multiply by the square root and it will become a whole number.

5 - sqrt(2)

--------------

sqrt(3)

Multiply the top and bottom by sqrt(3)

5 - sqrt(2)       sqrt(3)

--------------    * -----------

sqrt(3)             sqrt(3)

Distribute the sqrt(3) on top

5sqrt(3) - sqrt(2) sqrt(3)

-------------------------

sqrt(3)      *  sqrt(3)

5sqrt(3) - sqrt(6)

-------------------------

3

Rewriting

1/3 (5sqrt(3) - sqrt(6))

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