A number is multiplied 3 times by itself and then 61 is subtracted from the product obtained. If the final result is 9200, then the number is

Answer

To solve the problem step by step, we can follow these instructions:

### Step-by-Step Solution:

1. **Let the number be represented as \( x \)**:
- We start by defining the unknown number as \( x \).

2. **Set up the equation based on the problem statement**:
- According to the problem, the number is multiplied three times by itself, which means \( x \times x \times x \) or \( x^3 \).
- After multiplying, 61 is subtracted from this product, resulting in the equation:
\[ x^3 - 61 = 9200 \]

3. **Rearrange the equation**:
- To isolate \( x^3 \), we add 61 to both sides of the equation:
\[ x^3 = 9200 + 61 \]
- Simplifying this gives:
\[ x^3 = 9261 \]

4. **Find the cube root of both sides**:
- To find \( x \), we need to take the cube root of 9261:
\[ x = \sqrt[3]{9261} \]

5. **Calculate the cube root**:
- We can factor 9261 to find its cube root. Noticing that \( 21 \times 21 \times 21 = 9261 \), we find:
\[ x = 21 \]

6. **Conclusion**:
- Therefore, the required number is:
\[ \boxed{21} \]