Question
Simplify V 300. (1 point)
This radical expression is already
• fully simplified.
O 5/12
• 100/3
• 10/3
This radical expression is already
• fully simplified.
O 5/12
• 100/3
• 10/3
Answers
GPT-4o mini
To simplify \( V 300 \) (which I assume is the square root of 300, written as \( \sqrt{300} \)), we can break it down as follows:
1. Factor 300 into its prime factors:
\[
300 = 3 \times 100 = 3 \times 10^2 = 3 \times (2 \times 5)^2 = 3 \times 2^2 \times 5^2
\]
2. Now we can express \( \sqrt{300} \) in terms of its factors:
\[
\sqrt{300} = \sqrt{3 \times 100} = \sqrt{3} \times \sqrt{100} = \sqrt{3} \times 10 = 10\sqrt{3}
\]
Since \( 10\sqrt{3} \) is already simplified and does not lead to any of the answers provided (like \( \frac{5}{12} \), \( \frac{100}{3} \), or \( \frac{10}{3} \)), we need a method to approximate its value to see if it matches any of the answer choices.
Using the approximation \( \sqrt{3} \approx 1.732 \):
\[
10\sqrt{3} \approx 10 \times 1.732 \approx 17.32
\]
This does not directly relate to any of the fractions given.
To answer the question directly asking to simplify \( V 300 \) (assuming this means computing the square root), the result should be acknowledged as \( 10\sqrt{3} \).
Thus, consider the steps correctly:
- The answer \( 10\sqrt{3} \) does not match any of the given options, neither does the simplification yield any real fractions provided.
So, the correct interpretation and simplification leads us to recognize \( V(300) \) doesn't yield a straightforward single answer among your options. The most fitting conclusive result for \( \sqrt{300} \) is simply \( 10\sqrt{3} \).
1. Factor 300 into its prime factors:
\[
300 = 3 \times 100 = 3 \times 10^2 = 3 \times (2 \times 5)^2 = 3 \times 2^2 \times 5^2
\]
2. Now we can express \( \sqrt{300} \) in terms of its factors:
\[
\sqrt{300} = \sqrt{3 \times 100} = \sqrt{3} \times \sqrt{100} = \sqrt{3} \times 10 = 10\sqrt{3}
\]
Since \( 10\sqrt{3} \) is already simplified and does not lead to any of the answers provided (like \( \frac{5}{12} \), \( \frac{100}{3} \), or \( \frac{10}{3} \)), we need a method to approximate its value to see if it matches any of the answer choices.
Using the approximation \( \sqrt{3} \approx 1.732 \):
\[
10\sqrt{3} \approx 10 \times 1.732 \approx 17.32
\]
This does not directly relate to any of the fractions given.
To answer the question directly asking to simplify \( V 300 \) (assuming this means computing the square root), the result should be acknowledged as \( 10\sqrt{3} \).
Thus, consider the steps correctly:
- The answer \( 10\sqrt{3} \) does not match any of the given options, neither does the simplification yield any real fractions provided.
So, the correct interpretation and simplification leads us to recognize \( V(300) \) doesn't yield a straightforward single answer among your options. The most fitting conclusive result for \( \sqrt{300} \) is simply \( 10\sqrt{3} \).