Question

What is the quotient of the following expression? State the answer in simplest radical form. Rationalize the denominator if necessary. 5108√2125√ (1 point) Responses 315√5 the fraction with numerator 3 square root of 15 and denominator 5 15√9 the fraction with numerator square root of 15 and denominator 9 33–√ 3 square root of 3 303√105√

Answer 1

To simplify the expression \( \frac{5108 \sqrt{2125}}{\sqrt{1}} \) and find the quotient, we first need to look at the denominator.

Since the denominator is \( \sqrt{1} \), this simplifies to \( 1 \). Thus, we only need to simplify the numerator:

1. Simplify \( \sqrt{2125} \):

   • Factor \( 2125 \): \[ 2125 = 25 \times 85 = 25 \times 5 \times 17 \]
   • Take the square root: \[ \sqrt{2125} = \sqrt{25 \times 85} = \sqrt{25} \cdot \sqrt{85} = 5\sqrt{85} \]

2. Calculate \( 5108 \cdot 5\sqrt{85} \):

   • Multiply: \[ 5108 \cdot 5 = 25540 \]
   • Hence, we rewrite the expression: \[ \frac{5108 \cdot 5\sqrt{85}}{1} = 25540\sqrt{85} \]

3. Final result: Since \( 25540\sqrt{85} \) is not in the options provided, let's check if we need to simplify \( \fraction{3 \sqrt{15}}{5}, \frac{10}{3 \sqrt{3}}, or \frac{30}{3 \sqrt{105}} \).

However, it looks like we've missed interpreting the entire problem context about putting \( 5108 \sqrt{2125} \) against something.

Given what has been simplified with rational components, here's the breakdown into distinctive forms mentioned earlier.

• \( \frac{3\sqrt{15}}{5} \)
• \( 15\sqrt{9} = 15 \cdot 3 = 45\)
• \( 33 - \sqrt{3} \sqrt{3} = 33 - 3 = 30\)
• \( 30 \frac{\sqrt{105}}{2} \)

Finally, given successful attempts, the clean result after verification with denominator rationalizing doesn't yield neatly, do confirm which form, out of potentials attempt provide closest clean pairing and addresses radical across operations; from view above principles around roots and fractions simplification imply tentatively evaluated towards all forms.

Without error in path, provide clarity against complete re-evaluation of original components leading into final asserts you seek based on obtaining \( 25540\sqrt{85} \) through best evaluated quotient expectations. Validate through right expressions or roots plainly leading adjacent recognition expressed forms.

Let me know if any confusion prevails or if restructural adjustments to expressions continue towards clarification on preferences/pportuned criteria across operations!

Answer 2

which one is the answer

Answer 3

Let's clarify the problem and find the appropriate answer from the given options.

You mentioned the expression \( \frac{5108 \sqrt{2125}}{\sqrt{1}} \) which simplifies just to \( 5108 \sqrt{2125} \), and I simplified \( \sqrt{2125} \) to \( 5 \sqrt{85} \). This yields:

\[ 5108 \cdot 5 \sqrt{85} = 25540 \sqrt{85} \]

However, it seems you are likely working with a different expression based on the options provided.

Let's reason through the options provided:

1. Option 1: \(\frac{3\sqrt{15}}{5}\)
2. Option 2: \(\frac{15\sqrt{9}}{1} = 15 \times 3 = 45\)
3. Option 3: \(33 - \sqrt{3} \sqrt{3} = 33 - 3 = 30\)
4. Option 4: \(30\sqrt{105}\)

Since none of your provided options seem to result from the numbers from \(5108 \sqrt{2125}\) directly, it seems we might have misunderstood the initial expression from your question.

Can you clarify what expression you wanted to simplify or provide more context? If possible, please provide the original fraction or expression that was to be simplified so I can assist you accurately in determining which answer fits best from the provided options.