+68 1. Simplify sqrt108x^5y^8
2. Simplify (sqrt3) - (sqrt2)/(sqrt3) + (sqrt2)
3. Rewrite 32^5/3 as a radical expression and then simplify
+129845 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
