To find the width of the rectangular prism, we can start with the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given that the volume is 448 cubic centimeters, the height is 7 centimeters, and the length is equal to the width (let's denote both as \( x \)), we can set up the equation:
\[ 448 = x \times x \times 7 \]
This simplifies to:
\[ 448 = 7x^2 \]
Next, we can divide both sides by 7 to isolate \( x^2 \):
\[ \frac{448}{7} = x^2 \]
Calculating the left side:
\[ 64 = x^2 \]
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{64} \]
This gives us:
\[ x = 8 \]
Since \( x \) represents both the length and the width, the width of the rectangular prism is:
\[ \boxed{8} , \text{centimeters} \]
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