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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Radical Equations

To solve an equation with a square root, we square both sides. To solve an equation with a cube root, we cube both sides. If the index of the radical is 4, we raise each side to the fourth power, and so on.

Example 1

Solve for x:

 Solution = 5 Step 1 Isolate the radical term. Subtract 2 from both sides. Step 2 Apply the Principle of Powers. = 3 Cube both sides. = 33 Step 3 Solve the resulting equation. Simplify. Add 5 to both sides. Divide both sides by 2.Step 4 Check the solution. 2x - 5 2x x = 27 = 32 = 16

So, the solution is x = 16.

Example 2

Solve for x:

 Solution = 8 Step 1 Isolate the radical term. Subtract 5 from both sides. Step 2 Apply the Principle of Powers. = 3 Raise both sides to the fourth power. = 34 Step 3 Solve the resulting equation.Simplify. Subtract 9 from both sides. Divide both sides by 6.Step 4 Check the solution. The check is in the side note. So, the solution is x = 12. 6x + 9 6x x = 81 = 72 = 12