Square Root Function

Algebra-1

1. Fundamental Concepts

Definition: A square root function is a function of the form where the output is the non-negative value which, when multiplied by itself, gives the input.
Domain: The domain of the square root function is all real numbers greater than or equal to zero ( ).
Range: The range of the square root function is all non-negative real numbers ( ).

2. Key Concepts

Evaluating Square Roots:

Solving Equations: To solve , square both sides:

Graphing: The graph of starts at (0, 0) and increases as x increases.

3. Examples

Example 1 (Basic)

Problem: Evaluate

Step-by-Step Solution:

The square root of 16 is the number that, when squared, equals 16. This number is 4.

Validation: Substitute into original expression → ✓

Example 2 (Intermediate)

Problem: Solve for x in

Step-by-Step Solution:

Square both sides of the equation:
This simplifies to:

Validation: Substitute x=25 into original equation → ✓

4. Problem-Solving Techniques

Isolate the Square Root: Always isolate the square root term on one side of the equation before squaring both sides.
Check Solutions: After solving, substitute the solutions back into the original equation to ensure they are valid (i.e., they do not make the radicand negative).
Graphical Interpretation: Use graphs to visualize the behavior of square root functions and understand their domains and ranges.