How do you simplify #(4+3sqrt2)/(-3-sqrt5)#?

1 Answer
Jul 2, 2018

Answer:

#=> -3 + ( -9sqrt2 + 4sqrt5 + 3sqrt10)/4#

Explanation:

#(4 + 3Sqrt2) / (-3 - sqrt5)#

#"Multiply and divide by the conjugate "(-3 + sqrt5) " of the denominator."#

#=> ((4 + 3sqrt2 ) ( -3 + sqrt5)) / ((-3-sqrt5)(-3 + sqrt5))#

#=> (-12 -9sqrt2 + 4sqrt5 + 3sqrt10) / (9 - 5)#

#=> (-12 -9sqrt2 + 4sqrt5 + 3sqrt10)/4#