Simplify the radical expression (5+√3)(5-√3)
a. 16
b. 22
c. 25+10√3
d. 16+10√3
1 answer:
The given expression is in the form (a+b)(a-b) where
a = 5
b = sqrt(3)
Recall that
(a+b)(a-b) = a^2-b^2
is the difference of squares formula
If a = 5, then a^2 = 25
If b = sqrt(3), then b^2 = (sqrt(3))^2 = 3
The squaring undoes the square root. The two opposites cancel out.
So using a^2 = 25 and b^2 = 3, we can say
(a+b)(a-b) = a^2-b^2 = 25-3 = 22
Therefore,
(5+sqrt(3))(5-sqrt(3)) = 22
Answer: B) 22
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