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

1200√/50√
no explaining

7 answers

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

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

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: \[ 20\sqrt{3} \]

that is wrong

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.

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

8√27/2√45

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: \[ \frac{4\sqrt{15}}{5} \]