Find the cube-roots of :
9261

Answer

To find the cube root of 9261, we can follow these steps:

### Step 1: Factor the number 9261
We start by finding the prime factors of 9261.

- Check if 9261 is divisible by 3:
- Sum of digits: 9 + 2 + 6 + 1 = 18 (which is divisible by 3)
- Divide: 9261 ÷ 3 = 3087

- Check if 3087 is divisible by 3:
- Sum of digits: 3 + 0 + 8 + 7 = 18 (which is divisible by 3)
- Divide: 3087 ÷ 3 = 1029

- Check if 1029 is divisible by 3:
- Sum of digits: 1 + 0 + 2 + 9 = 12 (which is divisible by 3)
- Divide: 1029 ÷ 3 = 343

- Check if 343 is divisible by 7:
- 343 ÷ 7 = 49
- 49 ÷ 7 = 7
- 7 ÷ 7 = 1

So, the prime factorization of 9261 is:
\[ 9261 = 3^3 \times 7^3 \]

### Step 2: Apply the cube root
Now that we have the prime factorization, we can find the cube root:
\[ \sqrt[3]{9261} = \sqrt[3]{3^3 \times 7^3} \]

Using the property of cube roots:
\[ \sqrt[3]{a^3} = a \]
We can simplify:
\[ \sqrt[3]{3^3} \times \sqrt[3]{7^3} = 3 \times 7 \]

### Step 3: Calculate the final result
Now we multiply the results:
\[ 3 \times 7 = 21 \]

Thus, the cube root of 9261 is:
\[ \sqrt[3]{9261} = 21 \]

### Final Answer
The cube root of 9261 is **21**.

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