To rearrange equations with square roots, the key is to isolate the square root term and then use the inverse operation, which is squaring, to eliminate the square root (Reference: ![Part of a video titled Level 2 Algebra - Rearranging equations with square root signs]()).
Here's a step-by-step guide:
- Isolate the Square Root: Get the term with the square root by itself on one side of the equation. This might involve adding, subtracting, multiplying, or dividing other terms.
- Square Both Sides: Square both sides of the equation. This will eliminate the square root. Remember that (√x)² = x.
- Solve for the Variable: After squaring, solve the resulting equation for the variable you're trying to isolate. This might involve further algebraic manipulation.
Example:
Let's say we have the equation: √(x + 2) = 3
- Step 1: Isolate the square root. In this case, the square root is already isolated.
- Step 2: Square both sides.
(√(x + 2))² = 3²
x + 2 = 9 - Step 3: Solve for x.
x = 9 - 2
x = 7
Important Considerations:
- Extraneous Solutions: When you square both sides of an equation, you might introduce extraneous solutions (solutions that don't actually satisfy the original equation). Always check your solutions by plugging them back into the original equation to make sure they are valid.
- More Complex Equations: If you have multiple square roots or other terms mixed in, you might need to repeat these steps multiple times to isolate and eliminate all the square roots.
