How to Solve a Radical Equation

Step-by-step solution

1. Square both sides.

   $$\left(\sqrt{x + 5}\right)^2 = 4^2$$

   Why: Squaring undoes the square root.

2. Simplify both sides.

   $$x + 5 = 16$$

   Why: The left side becomes x + 5 and the right side becomes 16.

3. Subtract 5 from both sides.

   $$x = 11$$

   Why: Subtracting undoes the addition.

4. Check the answer in the original equation.

   $$\sqrt{11 + 5} = \sqrt{16} = 4$$

   Why: Squaring can create false solutions, so every answer needs a check.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\sqrt{x + 2} = 3$

   Show answer

   $x = 7$

2. 2

   $\sqrt{x - 4} = 5$

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   $x = 29$

3. 3

   $\sqrt{2x + 1} = 5$

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   $x = 12$

4. 4

   $\sqrt{x} = 9$

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   $x = 81$

5. 5

   $\sqrt{3x - 2} = 4$

   Show answer

   $x = 6$