Question

(sqrt6 + sqrt3)(sqrt2 - 2)

Answer 1

Using the distributive property, we can expand this expression:

(sqrt6 + sqrt3)(sqrt2 - 2) = sqrt6 * sqrt2 + sqrt6 * (-2) + sqrt3 * sqrt2 + sqrt3 * (-2)

To simplify this expression, we need to use the properties of square roots. Specifically, we can use the fact that sqrt(a) * sqrt(b) = sqrt(ab). Using this property, we can simplify each term:

sqrt6 * sqrt2 = sqrt(6*2) = sqrt12
sqrt6 * (-2) = -2 * sqrt6
sqrt3 * sqrt2 = sqrt(3*2) = sqrt6
sqrt3 * (-2) = -2 * sqrt3

Putting these simplifications together, we get:

sqrt6 * sqrt2 + sqrt6 * (-2) + sqrt3 * sqrt2 + sqrt3 * (-2) = sqrt12 - 2sqrt6 + sqrt6 - 2sqrt3

This expression cannot be simplified any further, so we can leave our answer in this form.