Simplify sqrt108x^5y^8

1. Simplify sqrt108x^5y^8

I'm assuming that x and y are positive

√[ 108 x^5 y^8]  =  √[36 *3 * x^4 * x * y^8 ] =  6x^2y^4 √ [ 3x]

2. Simplify (sqrt3) - (sqrt2)/(sqrt3) + (sqrt2)

[ √3 - √2 ] / [ √3 + √2 ]       multiply top/bottom by √3 - √2

 ( [ √3 - √2 ] [ √3 - √2 ] ) / ( [ √3 + √2 ] [ √3 - √2 ] )   =

( 3 - 2√6 + 2 ) / ( 3  - 2)  =

[ 5 - 2√6 ] / 1  =

[ 5 - 2√6 ]

3. Rewrite 32^5/3 as a radical expression and then simplify

32^(5/3)   =   ³√[ 32^5] = ³√[ (2^5)^5]  =  ³√[ 2^25]   = 2^8* ³√2  = 256 3√2