Question

What is the quotient of the following expression? State the answer in simplest radical form. Rationalize the denominator if necessary.

1200√/50√
no explaining

Answer 1

the answer should be resulting in a square root, an example being 12√6

Answer 2

that is wrong

Answer 3

What is the quotient of the following expression? State the answer in simplest radical form. Rationalize the denominator if necessary.

8√27/2√45

Answer 4

The quotient of the expression \( \frac{1200\sqrt{} }{50\sqrt{}} \) in simplest radical form is \( \frac{24\sqrt{}}{1} \) or \( 24\sqrt{} \).

Answer 5

I apologize for the oversight. Let's correct that.

Given the expression \( \frac{1200\sqrt{} }{50\sqrt{}} \):

1. Simplify the coefficients: \( \frac{1200}{50} = 24 \).
2. Multiply \( 1200 \) by the square root factor: \( \sqrt{1200} = \sqrt{100 \cdot 12} = 10\sqrt{12} \) since \( \sqrt{100} = 10 \).

Now putting it together:
\[
\frac{10\sqrt{12}}{1} = 10\sqrt{12}
\]

To simplify \( \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3} \):
Thus, \( 10\sqrt{12} = 10 \cdot 2\sqrt{3} = 20\sqrt{3} \).

So, the final answer is:
\[
20\sqrt{3}
\]

Answer 6

I apologize for the confusion in my previous responses. Let's correctly simplify the expression step by step this time.

We need to simplify \( \frac{1200\sqrt{}}{50\sqrt{}} \).

1. **Simplify the coefficients**:
\[
\frac{1200}{50} = 24
\]

2. **Now we express the square roots in the same form**:
\[
\frac{\sqrt{1200}}{\sqrt{50}} = \sqrt{\frac{1200}{50}} = \sqrt{24}
\]

3. **Combine the results**:
\[
24 \cdot \sqrt{24}
\]

4. **Simplifying \( \sqrt{24} \)**:
\[
\sqrt{24} = \sqrt{4 \cdot 6} = 2\sqrt{6}
\]

5. **Final expression**:
\[
24 \cdot 2\sqrt{6} = 48\sqrt{6}
\]

So, the final simplified result is:
\[
48\sqrt{6}
\]

Thank you for your patience, and I appreciate your understanding.

Answer 7

To simplify the expression \( \frac{8\sqrt{27}}{2\sqrt{45}} \), follow these steps:

1. **Simplify the coefficients**:
\[
\frac{8}{2} = 4
\]

2. **Simplify the square roots**:
- For \( \sqrt{27} \):
\[
\sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3}
\]
- For \( \sqrt{45} \):
\[
\sqrt{45} = \sqrt{9 \cdot 5} = 3\sqrt{5}
\]

3. **Substitute back into the expression**:
\[
\frac{8\sqrt{27}}{2\sqrt{45}} = \frac{4 \cdot 3\sqrt{3}}{3\sqrt{5}}
\]

4. **Cancel the common factors**:
\[
= \frac{4\sqrt{3}}{\sqrt{5}}
\]

5. **Rationalize the denominator**:
\[
= \frac{4\sqrt{3}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{4\sqrt{15}}{5}
\]

Thus, the final answer in simplest radical form is:
\[
\frac{4\sqrt{15}}{5}
\]