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First, isolate the term containing the radical.

Equation Containing Radicals: Solving Algebraically

Example 1 (one radical): Solve .5133 xx

5133 xx

Next, square both sided to remove the radical.

2510133 2 xxx

Now solve the resulting equation. 1270 2 xx

x = - 4, x = - 3Last, check each of these proposed solutions by substituting into the original equation.

531333 541343

Both check so the solution set is { - 4, - 3}.

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First rewrite the equation so the radicals are on opposite sides.

Equation Containing Radicals: Solving Algebraically

Slide 2

Example 2 (two radicals): Solve

.3812 xx

Next, square both sides.

3812 xx

986812 xxx

Since the equation now only contains one radical we can solve it by following the steps in the previous example; isolate the radical, etc.

86 xx

8362 xx

288362 xx

0288362 xx

x = 12, x = 24 Both check.

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The solution set is {- 7}.

Equation Containing Radicals: Solving Algebraically

Slide 3

Try to solve .5851 xx

Notes: If the equation of example 1 instead contained a cube root you would cube (not square) both sides once the radical term was isolated. It is not mandatory to check proposed solutions when raising both sides to an odd power. If an error has not been made, all the proposed solutions will check.

51333 xx

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Equation Containing Radicals: Solving Algebraically