Question

Evaluate roots quick check

Answer 1

It seems that you're asking for a quick check to evaluate roots, but I'm not entirely clear on what specific roots you're referring to—are they the square roots, cube roots, polynomial roots, or roots of equations?

However, I can provide a general outline for evaluating different types of roots:

### Square Roots
To evaluate the square root of a number \( x \):
- Familiarize yourself with perfect squares (e.g., \( \sqrt{1} = 1, \sqrt{4} = 2, \sqrt{9} = 3, \sqrt{16} = 4 \)).
- Use a calculator for non-perfect squares (e.g., \( \sqrt{2} \approx 1.414 \)).

### Cube Roots
To evaluate the cube root of a number \( x \):
- Recognize perfect cubes (e.g., \( \sqrt[3]{1} = 1, \sqrt[3]{8} = 2, \sqrt[3]{27} = 3 \)).
- For non-perfect cubes, use a calculator (e.g., \( \sqrt[3]{10} \approx 2.154 \)).

### Polynomial Roots
For polynomial equations (like \( ax^2 + bx + c = 0 \)):
1. **Quadratic Formula**: Use \( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \).
2. **Factoring**: Try to factor the polynomial, if possible.
3. **Graphical Methods**: Graph the polynomial to find where it crosses the x-axis.

### Example:
Evaluate the roots of \( x^2 - 5x + 6 = 0 \):
1. Factor the equation: \( (x - 2)(x - 3) = 0 \).
2. Set each factor to zero: \( x - 2 = 0 \) or \( x - 3 = 0 \).
3. Solve: \( x = 2 \) and \( x = 3 \).

### Quick Check Example:
Find the square root of \( 49 \):
- \( \sqrt{49} = 7 \) (since \( 7 \times 7 = 49 \)).

Please provide more specific details if you need assistance with a particular type of root or problem!