`root3(144) xx root3(12)` equals

Options

A. 12
B. 14
C. 13
D. 6

Answer

To solve the problem \( \sqrt[3]{144} \times \sqrt[3]{12} \), we can follow these steps:

### Step 1: Combine the Cube Roots
We can use the property of cube roots that states \( \sqrt[3]{a} \times \sqrt[3]{b} = \sqrt[3]{a \times b} \). Therefore, we can write:
\[ \sqrt[3]{144} \times \sqrt[3]{12} = \sqrt[3]{144 \times 12} \]

**Hint:** Remember the property of cube roots that allows you to combine them when multiplying.

### Step 2: Calculate the Product Inside the Cube Root
Now, we need to calculate \( 144 \times 12 \):
\[ 144 \times 12 = 1728 \]

**Hint:** You can break down the multiplication into smaller parts if it helps. For example, \( 144 \times 10 + 144 \times 2 \).

### Step 3: Find the Cube Root of 1728
Next, we need to find \( \sqrt[3]{1728} \). We can do this by recognizing that:
\[ 1728 = 12^3 \]
Thus,
\[ \sqrt[3]{1728} = \sqrt[3]{12^3} = 12 \]

**Hint:** Knowing perfect cubes can help you quickly find cube roots.

### Final Answer
So, the final answer is:
\[ \sqrt[3]{144} \times \sqrt[3]{12} = 12 \]

### Summary of Steps:
1. Combine the cube roots into one.
2. Calculate the product inside the cube root.
3. Find the cube root of the resulting number.