To rewrite the expression \( 100\sqrt{3}/2 \) as a product of identical factors, you can simplify it first:
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Simplify \( 100/2 \): \[ 100/2 = 50 \]
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Now the expression becomes: \[ 50\sqrt{3} \]
Next, we can write \( 50 \) as a product of identical factors:
\[ 50 = \sqrt{2500} \]
Thus, we can express \( 50\sqrt{3} \) as follows: \[ 50\sqrt{3} = \sqrt{2500}\sqrt{3} = \sqrt{2500 \times 3} = \sqrt{7500} \]
So we can rewrite \( 100\sqrt{3}/2 \) as: \[ \sqrt{7500} \]
If your goal is to express \( 100\sqrt{3}/2 \) in the form of identical factors, we have: \[ 50\sqrt{3} = x^2 \quad \text{where} \quad x = \sqrt{50\sqrt{3}} \]
To summarize, the expression \( 100\sqrt{3}/2 \) simplifies to \( 50\sqrt{3} \), which can be represented as \( \sqrt{7500} \) or \( \sqrt{(50\sqrt{3})^2} \).
If you are looking for a direct product form, we conclude: \[ 50\sqrt{3} = 5\sqrt{3} \cdot 10 \] or \[ \sqrt{50\sqrt{3}} \cdot \sqrt{50\sqrt{3}} = 50\sqrt{3} \] As a result, the expression contained within the product can be taken directly as \(( 5\sqrt{3} \cdot 10 )\) or written with identical factors as \(\sqrt{7500}\).
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