Express the product (sqrt2 -sqrt3) (sqrt2 - sqrt3) in simplest form.

Answer 1

To find the product of (sqrt2 - sqrt3) (sqrt2 - sqrt3), we can use the FOIL method (First, Outer, Inner, Last):

(sqrt2 - sqrt3) (sqrt2 - sqrt3) = sqrt2(sqrt2) - sqrt2(sqrt3) - sqrt3(sqrt2) + sqrt3(sqrt3)
= 2 - sqrt6 - sqrt6 + 3
= 5 - 2sqrt6

Therefore, the product of (sqrt2 - sqrt3) (sqrt2 - sqrt3) in simplest form is 5 - 2sqrt6.