Solving Radical Functions

Radical functions involve roots, such as square roots. To solve equations with radical expressions, we often isolate the radical on one side and then eliminate it by raising both sides to the appropriate power.

Example

Solve the equation: $\sqrt{x + 3} = 5$

1. Isolate the radical: The radical is already isolated on the left side.

2. Square both sides to eliminate the square root: $\left(\sqrt{x + 3}\right)^{2} = 5^{2}$

3. Simplify: $x + 3 = 25$

4. Subtract 3 from both sides: $x = 25 - 3$

5. Simplify: $x = 22$

6. Check the solution by substituting back into the original equation: $\sqrt{22 + 3} = \sqrt{25} = 5$ (This is correct.)

Thus, the solution to the equation is $x = 22$.

Key Questions

• What steps would you take to solve $\sqrt{2x - 1} = 3$?
• How do you check your solution after solving a radical equation?
• Why is it important to consider extraneous solutions when solving radical equations?
• Can you solve $\sqrt{x + 5} + 2 = 6$? What is the solution?

Keywords

• Radical functions
• Square root
• Isolate
• Extraneous solutions
• Solve