https://file.aiquickdraw.com/mathbot/file/17267373307158vemj8if.jpg

The OCR result was unclear, but from your image, I see the equation:

\[
\sqrt{7} - 2 = \sqrt{p - \sqrt{q}}
\]

Let's solve this equation step-by-step to find \( p \) and \( q \).

### Step 1: Square both sides to remove the square roots.

\[
(\sqrt{7} - 2)^2 = \left( \sqrt{p - \sqrt{q}} \right)^2
\]

On the left side:
\[
(\sqrt{7} - 2)^2 = (\sqrt{7})^2 - 2 \times \sqrt{7} \times 2 + 2^2 = 7 - 4\sqrt{7} + 4 = 11 - 4\sqrt{7}
\]

On the right side:
\[
\left( \sqrt{p - \sqrt{q}} \right)^2 = p - \sqrt{q}
\]

Thus, the equation becomes:
\[
11 - 4\sqrt{7} = p - \sqrt{q}
\]

### Step 2: Compare terms on both sides.

- The constant part \( p \) must match the constant term on the left side, so:
  \[
  p = 11
  \]
  
- The term involving the square root \( \sqrt{7} \) must match, so:
  \[
  -\sqrt{q} = -4\sqrt{7} \quad \Rightarrow \quad \sqrt{q} = 4\sqrt{7}
  \]
  Squaring both sides:
  \[
  q = (4\sqrt{7})^2 = 16 \times 7 = 112
  \]

Thus, the values of \( p \) and \( q \) are:
\[
p = 11, \quad q = 112
\]

Would you like any more details or clarifications on this?

Here are some related questions for further practice:
1. What happens if the right side has a different constant term?
2. How would the solution change if there was a coefficient in front of \( \sqrt{q} \)?
3. What if the equation involved cube roots instead of square roots?
4. How do you handle similar equations where both sides have different nested radicals?
5. Can this equation be solved graphically by plotting both sides?

**Tip:** When solving radical equations, always check for extraneous solutions by substituting the values back into the original equation.

Find p and q such that √7 - 2 = √(p - √q)

Learn how to solve the radical equation √7 - 2 = √(p - √q) step-by-step. This problem involves using properties of square roots and algebraic manipulations to determine the values of p and q. Suitable for high school students in Grades 10-12.

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