How do you simplify (sqrt5+2sqrt2)/(4-sqrt5)?

1 Answer
Dwight
Jan 15, 2017

Use the conjugate of the denominator to turn it into a whole number. Details below...

Explanation:

The first thing you want to do is eliminate the radical expression in the denominator. To do this, multiply top and bottom by the conjugate of the denominator, namely 4+sqrt5

((sqrt5 + 2sqrt2)(4+sqrt5))/((4-sqrt5)(4+sqrt5))

Use the FOIL method to multiply top and bottom

(4sqrt5+5+8sqrt2+2sqrt10)/(16-5)

(4sqrt5+5+8sqrt2+2sqrt10)/11

I think that is all you can do!

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