Step 1: Isolate the Radical by moving everything else
Step 1: Isolate the Radical by moving everything else
to the other side of the equation.
Move any term that is not under the radical to the other side using
Opposite Operations.
Step 2: Square both sides
If it is a third root, cube both sides, a fourth root? raise to the fourth power, etc.
It is a good idea to write parentheses around the terms
* If there are two terms remember to use FOIL or one of the formulas*
Step 3: Simplify each side
Write terms in descending order (highest power to lowest)
Distribute, Add or Subtract like terms.
Step 4: Solve for x
See notes for solving quadratic equations
Step 5: Repeat steps 1 through 4 if there is
more than one radical in the equation.
Formulas:
Two Terms:
Difference of Two Squares: a2 – b2 = (a – b)(a + b)
Difference of Two Cubes: a3 – b3 = (a – b)(a2 + ab + b2 )
Sum of Two Cubes: a3 + b3 = (a + b)(a2 – ab + b2 )
Three Terms: Perfect Square Trinomials
(Addition): (a + b)2 = a2 + ab + b2
(Subtraction) : (a – b)2 = a2 – ab + b2
Examples:
1) [pic]= x – 5 ( Already isolated, square both sides
([pic])2 = (x – 5)2 ( Right side is (x – 5)(x – 5) so use FOIL or a formula
x + 2 = x2 – 10x + 25 ( Move all terms to the right side, left side = zero
0 = x2 – 10x + 23 ( Won’t factor, use the quadratic equation
x = [pic] = [pic]= [pic] = [pic] = [pic] = [pic]
= [pic] = [pic] (Reduce every term: divide by 2)
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ANSWER( 5 ( [pic]
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