Equations with Radicals Kathy Lydens Equations with Radicals

Equations with Radicals Kathy Lyden's Equations with Radicals

Steps to Solving Equations with Radicals • Isolate the radical • Square both sides of the equation (or raise to appropriate power) • Solve for the variable • Check all solutions. If the answer(s) does not work, the equation may not have a real number solution. Note: You can also use the properties of radicals to solve equations Kathy Lyden's Equations with Radicals 2

Radical Equations EXAMPLE 1 Example 1: use properties of radicals isolate the variable distributive property rationalize the denominator the conjugate of is when the two binomials in the denominator are multiplied out, the two center terms cancel each other Kathy Lyden's Equations with Radicals 3

EXAMPLE 1 page 2 expand the denominator distribute the numerator simplify the denominator reduce by common factor Check the solution in the original equation: distributive property on the right Kathy Lyden's Equations with Radicals 4

Radical Equations EXAMPLE 2 Example 2: isolate the radical square both sides solve for the variable Check the solution in the original equation: The answer does not check in the original equation, therefore there are no real number solutions. Kathy Lyden's Equations with Radicals

Radical Equations EXAMPLE 3 Example 3: isolate the radical square both sides solve for the variable Check the solution in the original equation: Kathy Lyden's Equations with Radicals 6

Radical Equations EXAMPLE 4 Example 4: isolate one of the radicals square both sides / / isolate the radical square both sides Kathy Lyden's Equations with Radicals 7

EXAMPLE 4 page 2 solve for the variable Check the solution in the original equation: Kathy Lyden's Equations with Radicals 8

Equations with Radicals: EXERCISES Solution 1. 2 x = 10 2. x + x = 0 1. 2 x = 100 x = 50 square both sides x +x=0 isolate the radical (checks) x =-x x = x 2 0 = x 2 - x 0 = x(x - 1) x=0 and x=1 Kathy Lyden's Equations with Radicals square both sides isolate the variable factor and solve (only 0 checks)

Equations with Radicals: EXERCISES 2 Solution 3. y-7 =3 4. x - x-1 =3 3. y-7 =3 y - 7 = 27 y = 34 4. x - 1 = 3 - x-1=-x+3 x - 1 = x 2 - 6 x + 9 0 = x 2 - 7 x +10 0 = (x - 5)(x -2) x=5 and x =2 Kathy Lyden's Equations with Radicals cube both sides (checks) isolate the radical square both sides isolate the variable factor and solve (only 5 checks) 10

Equations with Radicals: EXERCISES 3 Solution 5. x-7 + 6. r = 3 x-3 =2 3 w 4 pd , 5. x-7 =2 - x-3 x-7=4 -4 x-3+x-3 -8=-4 x-3 2= x-3 4=x-3 7=x / / 3 for d 6. 3 w r = 4 pd 3 w r 3 = 4 pd r 3 = 3 w 3 w d = 4 pr 3 Kathy Lyden's Equations with Radicals isolate one radical square both sides isolate the radical square both sides solve for the variable (checks) cube both sides isolate the variable d (checks) 11