Find the cubes of :
`2.1`

Answer

To find the cube of 2.1, we need to multiply the number by itself three times. Here’s the step-by-step solution:

### Step 1: Write the expression for the cube
The cube of a number \( x \) is given by the expression:
\[ x^3 = x \times x \times x \]
For our case, we have:
\[ (2.1)^3 = 2.1 \times 2.1 \times 2.1 \]

### Step 2: Calculate \( 2.1 \times 2.1 \)
First, we will calculate \( 2.1 \times 2.1 \):
\[ 2.1 \times 2.1 = 4.41 \]
To do this, we can ignore the decimal point initially and multiply 21 by 21:
- \( 21 \times 21 = 441 \)
- Since we have two decimal places in \( 2.1 \) (one from each \( 2.1 \)), we place the decimal point two places from the right in 441, giving us \( 4.41 \).

### Step 3: Multiply the result by 2.1
Now we need to multiply \( 4.41 \) by \( 2.1 \):
\[ 4.41 \times 2.1 \]
Again, we can ignore the decimal point initially and multiply:
- \( 441 \times 21 \)

Calculating \( 441 \times 21 \):
1. \( 441 \times 1 = 441 \)
2. \( 441 \times 20 = 8820 \) (since \( 441 \times 2 = 882 \), we just add a zero)
3. Now, add these two results together:
\[ 441 + 8820 = 9261 \]

### Step 4: Place the decimal point
Since we have one decimal place in \( 2.1 \) and two decimal places in \( 4.41 \), we have a total of three decimal places. Therefore, we place the decimal point three places from the right in \( 9261 \):
\[ 9261 \rightarrow 9.261 \]

### Final Answer
Thus, the cube of \( 2.1 \) is:
\[ (2.1)^3 = 9.261 \]