Evaluate `root3(3375)`

Options

A. 15
B. 25
C. 30
D. 35

Answer

To evaluate the cube root of 3375, we can follow these steps:

### Step 1: Prime Factorization of 3375
First, we need to find the prime factorization of 3375. We can do this by dividing 3375 by prime numbers.

- 3375 is odd, so we start with 3:
- 3375 ÷ 3 = 1125
- 1125 ÷ 3 = 375
- 375 ÷ 3 = 125
- Now, we divide 125 by 5:
- 125 ÷ 5 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1

So, the prime factorization of 3375 is:
\[ 3375 = 3^3 \times 5^3 \]

### Step 2: Apply the Cube Root
Now that we have the prime factorization, we can apply the cube root to each factor:
\[ \sqrt[3]{3375} = \sqrt[3]{3^3 \times 5^3} \]

Using the property of cube roots:
\[ \sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b} \]

We can separate the factors:
\[ \sqrt[3]{3^3} \times \sqrt[3]{5^3} \]

### Step 3: Simplify the Cube Roots
Now we can simplify:
\[ \sqrt[3]{3^3} = 3 \]
\[ \sqrt[3]{5^3} = 5 \]

So, we have:
\[ \sqrt[3]{3375} = 3 \times 5 \]

### Step 4: Calculate the Final Result
Now, we multiply the results:
\[ 3 \times 5 = 15 \]

Thus, the cube root of 3375 is:
\[ \sqrt[3]{3375} = 15 \]

### Final Answer
The cube root of 3375 is **15**.

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