Find the cube root of `2300 xx 5290`.

Answer

To find the cube root of \( 2300 \times 5290 \), we can follow these steps:

### Step 1: Break down the numbers
First, we can express \( 2300 \) and \( 5290 \) in a more manageable form.

\[ 2300 = 23 \times 100 = 23 \times 10^2 \]
\[ 5290 = 529 \times 10 = 23^2 \times 10 \]

### Step 2: Combine the two numbers
Now, we can multiply these two expressions together:

\[ 2300 \times 5290 = (23 \times 10^2) \times (23^2 \times 10) \]

### Step 3: Simplify the multiplication
When we multiply, we can combine the bases:

\[ = 23^{1 + 2} \times 10^{2 + 1} = 23^3 \times 10^3 \]

### Step 4: Take the cube root
Now we can take the cube root of the entire expression:

\[ \sqrt[3]{2300 \times 5290} = \sqrt[3]{23^3 \times 10^3} \]

### Step 5: Apply the cube root property
Using the property of cube roots, we can separate the terms:

\[ = \sqrt[3]{23^3} \times \sqrt[3]{10^3} \]

### Step 6: Simplify the cube roots
Since the cube root and the cube cancel each other out, we have:

\[ = 23 \times 10 \]

### Step 7: Calculate the final answer
Now we can calculate the final result:

\[ = 230 \]

Thus, the cube root of \( 2300 \times 5290 \) is \( 230 \).

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