Question

Find the square root of 96. (1 point)
• 16/6
O 4V6
•24
6V4
Answer
Find the cubic root of 96. (1 point)
• 2V12
0237
• 24/12
04/6
Answer
)
Find the cubic root of 189. (1 point)
• 9,21
• 2737
0307
• 377
Answer
Find the square root of 250. (1 point)
• 5\10
• 250
25\10
10/5
Answer
Find the square root of 128. (1 point)
• 4V2
• 2V4
0 164 x V2
0812
Answered by GPT-4o mini
To find the square root of 96, we can simplify it as follows:

\[
\sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}
\]

So the correct answer is:

**4√6**.
Answered by GPT-4o mini
To find the cubic root of 96, we can simplify it as follows:

First, we can factor 96:

\[
96 = 2^5 \times 3^1
\]

Now, we can find the cubic root:

\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1}
\]

Using the property of roots, we can separate the terms:

\[
\sqrt[3]{96} = \sqrt[3]{2^5} \times \sqrt[3]{3^1}
\]

Calculating each part separately:

- \( \sqrt[3]{2^5} = 2^{5/3} = 2^{1 + 2/3} = 2 \times \sqrt[3]{4} \)
- \( \sqrt[3]{3^1} = \sqrt[3]{3} \)

So:

\[
\sqrt[3]{96} = 2 \times \sqrt[3]{4} \times \sqrt[3]{3} = 2 \times \sqrt[3]{12}
\]

Thus, the cubic root of 96 simplifies to:

\[
2 \sqrt[3]{12}
\]

The closest answer from your options is:

**2V12** (assuming "V" means the cubic root symbol).
Answered by GPT-4o mini
To find the cubic root of 189, we start with the prime factorization:

\[
189 = 3^3 \times 7
\]

Thus, we can write:

\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7} = \sqrt[3]{3^3} \times \sqrt[3]{7} = 3 \times \sqrt[3]{7}
\]

So the cubic root of 189 is:

\[
3 \sqrt[3]{7}
\]

None of the options provided directly match this result, so if you are looking for approximate decimal values, we can estimate:

\[
\sqrt[3]{7} \approx 1.913
\]

Thus,

\[
3 \times 1.913 \approx 5.739
\]

Which is not a match with any options, so based on the exact expression, the answer is \(3 \sqrt[3]{7}\). If there’s an error in interpreting the options, please clarify how they relate to expressions or decimal approximations!
Answered by GPT-4o mini
To find the square root of 250, we can simplify it as follows:

First, factor 250:

\[
250 = 25 \times 10 = 5^2 \times 10
\]

Now, we can take the square root:

\[
\sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \times \sqrt{10} = 5\sqrt{10}
\]

So the correct answer is:

**5√10**.

If you meant that option formatting (e.g., "5\10") represents this expression, then it is the closest matching result. If that is not one of the provided formats, please clarify!
Answered by GPT-4o mini
To find the square root of 128, we can simplify it as follows:

First, we can factor 128:

\[
128 = 64 \times 2 = 8^2 \times 2 = 4^3 \times 2
\]

Now we can take the square root:

\[
\sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}
\]

Alternatively, you can also express this as:

\[
\sqrt{128} = \sqrt{16 \times 8} = \sqrt{16} \times \sqrt{8} = 4 \times 2\sqrt{2} = 8\sqrt{2}
\]

So the correct answer, simplified, is:

**8√2.**

From your options, none exactly match \(8\sqrt{2}\). However, if any of the options might need clarification or correction, please let me know! The option **4V2** (which could mean \(4\sqrt{2}\)) does not accurately reflect the square root of 128 as per simplification shown above. If one of the options is intended to represent \(8\sqrt{2}\), please clarify!