Simplify the radical expression (5+√3) (5-√3)

a. 16

b. 22

c. 25+10√3

d. 16+10√3

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