Then what if it's under square root like √(x²-35)

If the expression is under a square root, such as \( \sqrt{x^2 - 35} \), the approach will differ based on whether you need to simplify, solve, or evaluate the expression. Let's break down the different scenarios.

### Simplifying \( \sqrt{x^2 - 35} \)

1. **Recognize the expression:** \( \sqrt{x^2 - 35} \) is already in its simplest form because there are no algebraic manipulations that can further simplify it without additional information about \( x \).

### Solving \( \sqrt{x^2 - 35} = 0 \)

If you are asked to solve the equation:

\[ \sqrt{x^2 - 35} = 0 \]

Here's the step-by-step process:

1. **Isolate the square root:**
   \[ \sqrt{x^2 - 35} = 0 \]

2. **Square both sides to eliminate the square root:**
   \[ (\sqrt{x^2 - 35})^2 = 0^2 \]
   \[ x^2 - 35 = 0 \]

3. **Solve the resulting quadratic equation:**
   \[ x^2 - 35 = 0 \]
   \[ x^2 = 35 \]
   \[ x = \pm \sqrt{35} \]

So, the solutions are:
\[ x = \sqrt{35} \]
\[ x = -\sqrt{35} \]

### Evaluating \( \sqrt{x^2 - 35} \)

If you are asked to evaluate \( \sqrt{x^2 - 35} \) for a specific value of \( x \):

1. **Substitute the given value of \( x \) into the expression.**

For example, if \( x = 7 \):
\[ \sqrt{x^2 - 35} = \sqrt{7^2 - 35} = \sqrt{49 - 35} = \sqrt{14} \]

### Summary of Different Scenarios

1. **Simplifying:** \( \sqrt{x^2 - 35} \) is already in simplest form.
2. **Solving \( \sqrt{x^2 - 35} = 0 \):**
   - Set the expression equal to zero and solve the resulting quadratic equation.
   - Solutions: \( x = \pm \sqrt{35} \).
3. **Evaluating:** Substitute the given value of \( x \) and simplify.

Do you want more details or have any questions about this process?

Here are some questions you might want to ask next:
1. How do I solve equations involving square roots and variables?
2. What are the properties of square roots in algebra?
3. Can you explain how to rationalize expressions involving square roots?
4. How do I handle inequalities involving square roots?
5. Can you show examples of solving real-world problems using square root equations?

### Tip:
When dealing with square roots, remember that squaring both sides can help eliminate the square root, but be cautious as this can sometimes introduce extraneous solutions. Always check your solutions by substituting them back into the original equation.

Explore how to handle expressions under square roots like √(x² - 35). Learn to simplify, solve equations, and evaluate the expression. Suitable for advanced high school students and beyond.

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