Let's solve the equation step by step:

The given equation is:

\[
x - \sqrt{61 - 13} = 7
\]

### Step 1: Simplify the expression inside the square root
\[
61 - 13 = 48
\]

Now the equation becomes:
\[
x - \sqrt{48} = 7
\]

### Step 2: Simplify \(\sqrt{48}\)
\[
\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}
\]

So the equation becomes:
\[
x - 4\sqrt{3} = 7
\]

### Step 3: Solve for \(x\)
To isolate \(x\), add \(4\sqrt{3}\) to both sides:
\[
x = 7 + 4\sqrt{3}
\]

Thus, the solution is:
\[
x = 7 + 4\sqrt{3}
\]

If you need further simplifications or details, feel free to ask!

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Would you like more details on this or have any questions?  
Here are 5 related questions you might find interesting:

1. How do you rationalize a denominator with a square root?
2. How do you simplify radicals with higher powers?
3. What are the properties of square roots in algebraic expressions?
4. How do you handle equations involving higher-degree roots?
5. How do you approximate the value of irrational numbers?

**Tip:** Always simplify square roots first to make solving equations easier!

This step-by-step solution explains how to solve the equation x − (61 − 13)^0.5 = 7 by simplifying square roots and radicals. Learn the process of solving equations with radicals, including how to handle irrational numbers like √48. Suitable for students in Grades 9-11.

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