Solving Radical Equations in Algebra 2

What Are Radical Equations?

A radical equation contains a variable under a radical sign (square root). Example: \( \sqrt{2x+3} = 5 \).

How to Solve Radical Equations

1. Isolate the radical on one side of the equation.
2. Square both sides to eliminate the radical.
3. Solve the resulting equation.
4. Check for extraneous solutions ΓÇö squaring can introduce false solutions.

Example

Solve \( \sqrt{2x+3} = 5 \):

1. Square both sides: \( 2x + 3 = 25 \)
2. Subtract 3: \( 2x = 22 \)
3. Divide by 2: \( x = 11 \)
4. Check: \( \sqrt{22+3} = \sqrt{25} = 5 \) Γ£ô

Why Check for Extraneous Solutions?

Squaring both sides can create solutions that do not satisfy the original equation. Always substitute back to verify.

Try radical equations on our Algebra 2 Solver!