Question

Rewrite the expression as a product of identical factors to find the product for 100sqrd3/2

Answer 1

To rewrite the expression \( 100\sqrt{3}/2 \) as a product of identical factors, you can simplify it first:

1. Simplify \( 100/2 \):
\[
100/2 = 50
\]

2. 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 \(\sqrt{7500}\).