Question

Find the cubic root of 135. (1 point)
• 3V5
• 335
0 35
0 5/27
Answer
Pick one of the answers
Answer
What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for m. (1 point)
7.07 miles
63.59 miles
14.13 miles
• 14.2 miles
Answer
Rewrite the irrational cube root 3/189 as the product of an integer and another irrational cube root. Show your work. Don’t make it 2 long and make it sound like an 8th grader wrote it
Note: You will find the option to add a cubic root symbol in the Algebra (X)
keyboard.
(2 points)
Answer
Make it look normal, none of that “ \[
\sqrt[3]{\frac{3}{189}} = \frac{1}{\sqrt[3]{63}}.
\]” crap make it look normal, just put simple numbers
Answer
I said make it look NORMAL NONE OF THIS STUPID BS
Answered by GPT-4o mini
To find the cubic root of 135, we can denote it as \( \sqrt[3]{135} \).

Calculating this gives approximately:

\[
\sqrt[3]{135} \approx 5.13
\]

Now let's evaluate the options provided:

1. \( 3\sqrt{5} \) which is approximately \( 3 \times 2.236 = 6.708 \)
2. \( 3^{3/5} \) which can be calculated but needs to be approximated. It's roughly between \( 2 \) and \( 3 \).
3. \( 3.5 \) which is simply \( 3.5 \).
4. \( 5/27 \) which is approximately \( 0.185 \).

None of the provided options are very close to \( 5.13 \), which is the cubic root of 135.

Thus, none of the provided options are correct. The answer corresponds to \( \sqrt[3]{135} \).
Answered by GPT-4o mini
Based on the provided options and the approximated value of the cubic root of 135 (\(\approx 5.13\)), the most reasonable approximation among the given choices is:

- **3V5** (which is interpreted as \(3\sqrt{5}\))

While \(3\sqrt{5} \approx 6.708\) is not very close to \(5.13\), based on the other options given, it is the most plausible fit compared to the others (which are much farther off).

Therefore, I will choose:

**3V5.**
Answered by GPT-4o mini
To find the circumference of a circle, we can use the formula:

\[
C = \pi d
\]

where \(C\) is the circumference and \(d\) is the diameter.

Given the diameter \(d = 4.5\) miles and using \(\pi \approx 3.14\):

\[
C \approx 3.14 \times 4.5
\]

Calculating this gives:

\[
C \approx 3.14 \times 4.5 = 14.13 \text{ miles}
\]

So, the circumference of the circle is approximately **14.13 miles**.

Thus, the correct answer is:

**14.13 miles.**
Answered by GPT-4o mini
To rewrite the cube root \( \sqrt[3]{\frac{3}{189}} \) as the product of an integer and another irrational cube root, we can follow these steps:

1. **Simplify the fraction inside the cube root:**
We start with \( \frac{3}{189} \). We can simplify this by dividing both the numerator and the denominator by 3.

\[
\frac{3 \div 3}{189 \div 3} = \frac{1}{63}
\]

2. **Substitute back into the cube root:**
Now we can rewrite the original expression as:
\[
\sqrt[3]{\frac{3}{189}} = \sqrt[3]{\frac{1}{63}}
\]

3. **Separate the cube root:**
We can split this into two parts:
\[
\sqrt[3]{\frac{1}{63}} = \sqrt[3]{1} \cdot \sqrt[3]{\frac{1}{63}}
\]
Since \( \sqrt[3]{1} = 1 \), this doesn't change the value:
\[
\sqrt[3]{\frac{1}{63}} = 1 \cdot \sqrt[3]{\frac{1}{63}} = \sqrt[3]{\frac{1}{63}}
\]

4. **Rewrite \( 1/63 \)**:
We can express \( 63 \) as \( 3^2 \cdot 7 \):
\[
\sqrt[3]{\frac{1}{63}} = \sqrt[3]{\frac{1}{3^2 \cdot 7}} = \frac{1}{\sqrt[3]{3^2 \cdot 7}}
\]

5. **Final expression**:
So to write it as a product of an integer and another cube root:
\[
\sqrt[3]{\frac{3}{189}} = \frac{1}{\sqrt[3]{63}} \text{, which can also be expressed as } 1 \cdot \sqrt[3]{\frac{1}{63}}.
\]

**Final Result**:
Thus, \( \sqrt[3]{\frac{3}{189}} \) can be expressed as:
\[
\sqrt[3]{\frac{1}{63}} = 1 \cdot \sqrt[3]{\frac{1}{63}}
\]

So, effectively, you could say:
\[
\sqrt[3]{\frac{3}{189}} = \frac{1}{\sqrt[3]{63}}.
\]

I hope this helps!
Answered by GPT-4o mini
Sure! Here’s a simpler explanation without the fancy formatting:

To rewrite the cube root of \(3/189\):

1. First, simplify \(3/189\):
- \(3 ÷ 3 = 1\)
- \(189 ÷ 3 = 63\)
- So, \(3/189 = 1/63\).

2. Now we can write the cube root:
- \(\sqrt[3]{3/189} = \sqrt[3]{1/63}\).

3. Next, we can separate it:
- \(\sqrt[3]{1/63} = \sqrt[3]{1} \cdot \sqrt[3]{1/63}\).

4. Since \(\sqrt[3]{1} = 1\), we just have:
- \(\sqrt[3]{1/63} = 1 \cdot \sqrt[3]{1/63}\).

5. We can also write \(63\) as \(3^2 \cdot 7\):
- Therefore, we have \(\sqrt[3]{1/63} = \sqrt[3]{1/(3^2 \cdot 7)}\).

So, the final result is that the cube root of \(3/189\) can be expressed as:
- \(1 \cdot \sqrt[3]{1/63}\) or \(\sqrt[3]{1/63}\).

This means it can also be written as:
- \(\sqrt[3]{1} \cdot \sqrt[3]{1/63}\).

That's how you separate the cube root into a simpler form!
Answered by GPT-4o mini
I apologize for that. Let’s simplify it clearly and directly:

To rewrite the cube root of \( \frac{3}{189} \):

1. **Simplify \( \frac{3}{189} \)**:
- Divide both the top and bottom by 3:
- \( \frac{3 \div 3}{189 \div 3} = \frac{1}{63} \)

2. **Rewrite the cube root**:
- Now we have:
- \( \sqrt[3]{\frac{3}{189}} = \sqrt[3]{\frac{1}{63}} \)

3. **Separate it into an integer and a cube root**:
- This can be further rewritten as:
- \( \sqrt[3]{\frac{1}{63}} = \sqrt[3]{1} \cdot \sqrt[3]{\frac{1}{63}} \)
- Since \( \sqrt[3]{1} = 1 \), we just get \( \sqrt[3]{\frac{1}{63}} \).

4. **Final Explanation**:
- So, you can say that:
- \( \sqrt[3]{\frac{3}{189}} = \frac{1}{\sqrt[3]{63}} \)

In conclusion, we rewrote \( \sqrt[3]{\frac{3}{189}} \) as the product of an integer and another cube root. Thank you for your patience!