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25 May, 21:32

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

a. 16

b. 22

c. 25+10√3

d. 16+10√3

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Answers (1)
  1. 25 May, 23:31
    0
    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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