simplify the product: sqrt6 (sqrt2 + sqrt3)
To simplify the product:
sqrt6 (sqrt2 + sqrt3)
Distribute sqrt6:
= sqrt6 * sqrt2 + sqrt6 * sqrt3
Simplify each term by multiplying the square roots:
= sqrt(6*2) + sqrt(6*3)
= sqrt(12) + sqrt(18)
Simplify the square roots by factoring out the perfect squares:
= sqrt(4*3) + sqrt(9*2)
= 2sqrt3 + 3sqrt2
Therefore, the simplified product is 2sqrt(3) + 3sqrt(2).