Cube root of a number when divided by 5 results in 25 what is the number?

Options

A. 5
B. `125^(3)`
C. `5^(2)`
D. `125`

Answer

To solve the problem step by step, let's denote the unknown number as \( x \).

### Step 1: Set up the equation
According to the problem, the cube root of the number \( x \) when divided by 5 equals 25. We can express this mathematically as:
\[ \frac{\sqrt[3]{x}}{5} = 25 \]

### Step 2: Multiply both sides by 5
To eliminate the fraction, we multiply both sides of the equation by 5:
\[ \sqrt[3]{x} = 25 \times 5 \]
Calculating the right side gives:
\[ \sqrt[3]{x} = 125 \]

### Step 3: Cube both sides
Next, we will cube both sides to solve for \( x \):
\[ x = 125^3 \]

### Step 4: Calculate \( 125^3 \)
Now we need to calculate \( 125^3 \). We can do this step by step:
\[ 125 \times 125 = 15625 \]
Now multiply this result by 125:
\[ 15625 \times 125 = 1953125 \]

Thus, we find:
\[ x = 1953125 \]

### Final Answer
The number is \( 1953125 \).

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