SOLUTION: how do you solve (5+ square root6)(5-square root2)

Question 1004699: how do you solve (5+ square root6)(5-square root2)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the problem is:

(5 + sqrt(6)) * (5-sqrt(2))

you would multiply these using the distributive law of multiplication, same as you would any other multiplication of this type.

distributive law of multiplication says:

(a + b) * (c + d) = ac + ad + bc + bd

in this problem that becomes:

(5 + sqrt(6)) * (5-sqrt(2)) = 5 * 5 - 5 * sqrt(2) + sqrt(6) * 5 - sqrt(6)*sqrt(2)

you would then simplify:

5*5 = 25
5 * sqrt(2) = 5 * sqrt(2)
sqrt(6) * 5 = 5 * sqrt(6)
sqrt(6)*sqrt(2) = sqrt(6*2) = sqrt(12) = sqrt(4*3) = 2*sqrt(3)

put them all together and you get:

(5 + sqrt(6)) * (5-sqrt(2)) = 5 * 5 - 5 * sqrt(2) + sqrt(6) * 5 - sqrt(6)*sqrt(2) becomes:

(5 + sqrt(6)) * (5-sqrt(2)) = 25 - 5 * sqrt(2) + 5 * sqrt(6) - 2 * sqrt(3)

there are no common terms that can be combined any further.

i believe this is as simple as it can get.

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