SOLUTION: Multiply: (5√[2] + 3)(√[2] – 2√[3])

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Question 111589: Multiply:
(5√[2] + 3)(√[2] – 2√[3])
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply:
(5√[2] + 3)(√[2] – 2√[3])
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Use FOIL:
F: 5sqrt(2) * sqrt(2) = 10
O: 5sqrt(2) * -2sqrt(3) = -10sqrt(6)
I: 3 * sqrt(2) = 3sqrt(2)
L: 3*-2sqrt(3) = -6sqrt(3)
-----------------
Combine to get:
10(1-sqrt(6))+3(sqrt2-2sqrt(3)
==============
Comment: Are you sure that "3" in the problem you posted is
not really "sqrt(3)"??
===========
Cheers,
Stan H.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%285sqrt%282%29+%2B+sqrt%283%29%29%28sqrt%282%29-+sqrt%283%29%29


Since sqrt%282%29%2A+sqrt%282%29+=++%28sqrt%282%29%29%5E2+=+2, and sqrt%28a%29%2Asqrt%28b%29=sqrt%28ab%29 (in your case numbers are +real+and+positive)
then we have:
5%2A+2+-+5sqrt%282%2A3%29+%2B+3sqrt%282%2A3%29
10+-+5sqrt%286%29+%2B+3sqrt%286%29

10+-+2sqrt%286%29…………sqrt%286%29=+2.45
10+-+2%282.45%29
10+-+4.9
5.1

Note that
sqrt%28a%29%2Asqrt%28b%29=sqrt%28ab%29 is not necessarily true when dealing with numbers that are not+real+and+positive