(sqrt 5 sqrt 2 + 3 sqrt 2) / [ 2 sqrt 2 + sqrt ( 3 - sqrt 5) ]
sqrt 2(sqrt 5 + 3 ) / [ 2 sqrt 2 + sqrt ( 3 - sqrt 5) ]
I am suspicious that you mean
(sqrt 5 sqrt 2 + 3 sqrt 2) / [ 2 sqrt 2 * sqrt ( 3 - sqrt 5) ]
then
sqrt 2(sqrt 5 + 3 ) / [ 2 sqrt 2* sqrt ( 3 - sqrt 5) ]
(1/2) (3+sqrt 5)/ sqrt(3-sqrt 5)
multiply top and bottom by sqrt (3+sqrt5)
(1/2) (3+sqrt 5)^(3/2) / sqrt(3-sqrt 5)sqrt(3+sqrt 5)
(1/2) (3+sqrt 5)^(3/2) / sqrt(9-5)
(1/4) (3+sqrt 5)^3/2
Solve
(root10+root18)/(root8+(root(3-root5)))
Urgent
2 answers
(√10+√18)/(2√2+√(3-√5))
Note that
3-√5 = (5-2√5+1)/2 = 1/2 (√5-1)^2
so now you have
(√10+√18)/(2√2 + 1/√2 (√5-1))
√2(√5+3) /(√2 (2 + (√5-1)/2))
2(√5+3)/(4+√5-1)
2(3+√5)/(3+√5)
2
Note that
3-√5 = (5-2√5+1)/2 = 1/2 (√5-1)^2
so now you have
(√10+√18)/(2√2 + 1/√2 (√5-1))
√2(√5+3) /(√2 (2 + (√5-1)/2))
2(√5+3)/(4+√5-1)
2(3+√5)/(3+√5)
2