The cube root of 97336 is

Options

A. 17
B. 18
C. 46
D. 23

Answer

To find the cube root of 97336, we will perform the following steps:

### Step 1: Prime Factorization
We start by finding the prime factors of 97336.

1. Divide 97336 by 2 (the smallest prime number):
- 97336 ÷ 2 = 48668
2. Divide 48668 by 2:
- 48668 ÷ 2 = 24334
3. Divide 24334 by 2:
- 24334 ÷ 2 = 12167
4. Now, 12167 is not divisible by 2, so we try the next prime number, which is 3. It is also not divisible by 3. We check the next prime number, which is 23:
- 12167 ÷ 23 = 529
5. Next, we factor 529:
- 529 ÷ 23 = 23
6. Finally, we divide 23 by itself:
- 23 ÷ 23 = 1

Now, we have completed the prime factorization. The prime factorization of 97336 is:
\[ 97336 = 2^3 \times 23^3 \]

### Step 2: Finding the Cube Root
Now that we have the prime factorization, we can find the cube root of 97336.

Using the property of cube roots:
\[ \sqrt[3]{a^3} = a \]
We can apply this to our factorization:
\[ \sqrt[3]{97336} = \sqrt[3]{2^3 \times 23^3} \]
This simplifies to:
\[ \sqrt[3]{2^3} \times \sqrt[3]{23^3} = 2 \times 23 \]

### Step 3: Calculate the Result
Now we calculate:
\[ 2 \times 23 = 46 \]

Thus, the cube root of 97336 is **46**.

### Final Answer
The cube root of 97336 is **46**.

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