A few multiplying radical questions??

Question

1. (2 sqrt 7 + sqrt 3 ) ( 3 sqrt 7 - sqrt 2 )

2. ( 3 sqrt x^5 ) ( 2 sqrt x^3 )

3. (3 sqrt x ^3) ( 2 sqrt x^3 )

Answer 1

(2√7 + √3)(3√7 - √2) =

3√7 2√7 + 3√7 √3 - √2 2√7 - √2 √3 =

3 x 2 √49 + 3√21 - 2√14 - √6 =

6 x 7 + 3√21 - 2√14 - √6

42 + 3√21 - 2√14 - √6

- - - - - - - - -s-

Answer 2

1. (2 sqrt 7 + sqrt 3 ) ( 3 sqrt 7 - sqrt 2 ) =
= 2 sqrt 7 * 3 sqrt 7 + sqrt3 * 3sqrt7 - 2 sqrt7 * sqrt2 -
- sqrt 3 * sqrt 2 = 6*7 + 3 sqrt 21 - 2 sqrt 14 - sqrt 6 =
= 42 + 3 sqrt 21 - 2 sqrt 14 - sqrt 6

2. ( 3 sqrt x^5 ) ( 2 sqrt x^3 ) = 6 * sqrt (x^8) =
= 6 (x^4)
Note: x must be non-negative or you cannot take square roots of x^3 and x^5

3. (3 sqrt x ^3) ( 2 sqrt x^3 ) = 6 sqrt(x^6) = 6(x^3).
Again: x should not be negative.