How do you simplify (sqrt5+2sqrt2)/(4-sqrt5)√5+2√24−√5?

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+sqrt54+√5

((sqrt5 + 2sqrt2)(4+sqrt5))/((4-sqrt5)(4+sqrt5)) (√5+2√2)(4+√5)(4−√5)(4+√5)

Use the FOIL method to multiply top and bottom

(4sqrt5+5+8sqrt2+2sqrt10)/(16-5)4√5+5+8√2+2√1016−5

(4sqrt5+5+8sqrt2+2sqrt10)/114√5+5+8√2+2√1011

I think that is all you can do!

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