SOLUTION: Tell whether the statement is true or false. If it is false, give the correct answer and explain your answer. The easiest way to simplify the expression (fraction) 1 over 5 + the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Tell whether the statement is true or false. If it is false, give the correct answer and explain your answer. The easiest way to simplify the expression (fraction) 1 over 5 + the      Log On


   

Question 319731: Tell whether the statement is true or false. If it is false, give the correct answer and explain your answer. The easiest way to simplify the expression (fraction)
1 over 5 + the square root of 3 is to multiply both the numerator and denominator by 5 + square root of 3.
Answer by J2R2R(94) About Me  (Show Source):
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FALSE

Whenever you have a surd of the form (a + root b) as the denominator (a surd is an expression of the form a + root b) it is always easiest to multiply numerator and denominator by (a - root b) since this will make the denominator the difference of two squares and the square of a root eliminates the need to use roots in the denominator.

So,
1/(a + root b) = (a - root b)/((a - root b)(a + root b)) = (a - root b)/(a squared - b)

Therefore
1/(5 + root 3) = (5 - root 3)/((5 - root 3)(5 + root 3)) = (5 - root 3)/(25 - 3) = (5 - root 3)/22

We multiplied numerator and denominator by (5 - root 3)