Question
find the square root of 96.
6√4
16√6
24
4√6
6√4
16√6
24
4√6
Answers
Answer
find the cubic root of 96
4√6
2√12
2^3√7
2^√12
4√6
2√12
2^3√7
2^√12
Answer
please pick one
Answer
find the cubic root of 189.
27^3√7
3^3√7
9^3√21
3√7
27^3√7
3^3√7
9^3√21
3√7
Answer
find the square root of 250
25√10
250
5√10
10√5
25√10
250
5√10
10√5
Answer
find the square root of 128.
8√2
√64 x √2
4√2
2√4
8√2
√64 x √2
4√2
2√4
Answered by
GPT-4o mini
To find the square root of 96, we can start by simplifying the square root:
\[
\sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}
\]
So the square root of 96 is \( 4\sqrt{6} \).
Therefore, the correct answer is \( 4\sqrt{6} \).
\[
\sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}
\]
So the square root of 96 is \( 4\sqrt{6} \).
Therefore, the correct answer is \( 4\sqrt{6} \).
Answered by
GPT-4o mini
To find the cube root of 96, we can start by simplifying it:
\[
96 = 2^5 \times 3
\]
Now, we can compute the cube root:
\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3} = \sqrt[3]{2^5} \times \sqrt[3]{3}
\]
Since \( \sqrt[3]{2^5} = 2^{5/3} = 2^{1 + 2/3} = 2 \cdot 2^{2/3} = 2 \cdot \sqrt[3]{4} \)
So,
\[
\sqrt[3]{96} = 2 \cdot 2^{2/3} \cdot \sqrt[3]{3}
\]
However, an easier way to express \( \sqrt[3]{96} \) is not easily simplified further into the choices given.
Now let's check each of the provided options:
1. **\( 4\sqrt{6} \)** - This is not a cube root.
2. **\( 2\sqrt{12} \)** - This can be simplified to \( 2 \cdot 2\sqrt{3} = 4\sqrt{3} \), which is still not equal to the cube root.
3. **\( 2^{3}\sqrt{7} = 8\sqrt{7} \)** - This also does not match.
4. **\( 2^{\sqrt{12}} \)** - This is unrelated.
None of the options provided seem to match the cube root of 96 directly. The cube root of 96 is approximately \( \sqrt[3]{96} \approx 4.64 \), but in terms of simpler radicals, it remains \( 2 \sqrt[3]{12} \).
In this case, **none of the given options correctly represent the cube root of 96.**
\[
96 = 2^5 \times 3
\]
Now, we can compute the cube root:
\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3} = \sqrt[3]{2^5} \times \sqrt[3]{3}
\]
Since \( \sqrt[3]{2^5} = 2^{5/3} = 2^{1 + 2/3} = 2 \cdot 2^{2/3} = 2 \cdot \sqrt[3]{4} \)
So,
\[
\sqrt[3]{96} = 2 \cdot 2^{2/3} \cdot \sqrt[3]{3}
\]
However, an easier way to express \( \sqrt[3]{96} \) is not easily simplified further into the choices given.
Now let's check each of the provided options:
1. **\( 4\sqrt{6} \)** - This is not a cube root.
2. **\( 2\sqrt{12} \)** - This can be simplified to \( 2 \cdot 2\sqrt{3} = 4\sqrt{3} \), which is still not equal to the cube root.
3. **\( 2^{3}\sqrt{7} = 8\sqrt{7} \)** - This also does not match.
4. **\( 2^{\sqrt{12}} \)** - This is unrelated.
None of the options provided seem to match the cube root of 96 directly. The cube root of 96 is approximately \( \sqrt[3]{96} \approx 4.64 \), but in terms of simpler radicals, it remains \( 2 \sqrt[3]{12} \).
In this case, **none of the given options correctly represent the cube root of 96.**
Answered by
GPT-4o mini
Since none of the options directly equate to the cube root of 96, we will choose the option that is the closest in form or reasonable approximation.
Among the four options given:
1. \( 4\sqrt{6} \)
2. \( 2\sqrt{12} \)
3. \( 2^3\sqrt{7} \)
4. \( 2^{\sqrt{12}} \)
The best option to choose is **\( 2\sqrt{12} \)** since:
\[
2\sqrt{12} = 2 \cdot 2\sqrt{3} = 4\sqrt{3}
\]
This option, while not the exact cube root of 96, is the one that fits the structure better compared to other choices.
**So I will pick \( 2\sqrt{12} \).**
Among the four options given:
1. \( 4\sqrt{6} \)
2. \( 2\sqrt{12} \)
3. \( 2^3\sqrt{7} \)
4. \( 2^{\sqrt{12}} \)
The best option to choose is **\( 2\sqrt{12} \)** since:
\[
2\sqrt{12} = 2 \cdot 2\sqrt{3} = 4\sqrt{3}
\]
This option, while not the exact cube root of 96, is the one that fits the structure better compared to other choices.
**So I will pick \( 2\sqrt{12} \).**
Answered by
GPT-4o mini
To find the cube root of 189, we first factor 189:
\[
189 = 3^3 \times 7
\]
Now, we can express the cube root:
\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7} = \sqrt[3]{3^3} \times \sqrt[3]{7} = 3 \sqrt[3]{7}
\]
Now, let's look at the provided options:
1. \( 27 \sqrt[3]{7} \)
2. \( 3 \sqrt[3]{7} \)
3. \( 9 \sqrt[3]{21} \)
4. \( 3 \sqrt{7} \)
The correct answer is **\( 3 \sqrt[3]{7} \)**, which matches our calculation.
So, the cube root of 189 is **\( 3 \sqrt[3]{7} \)**.
\[
189 = 3^3 \times 7
\]
Now, we can express the cube root:
\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7} = \sqrt[3]{3^3} \times \sqrt[3]{7} = 3 \sqrt[3]{7}
\]
Now, let's look at the provided options:
1. \( 27 \sqrt[3]{7} \)
2. \( 3 \sqrt[3]{7} \)
3. \( 9 \sqrt[3]{21} \)
4. \( 3 \sqrt{7} \)
The correct answer is **\( 3 \sqrt[3]{7} \)**, which matches our calculation.
So, the cube root of 189 is **\( 3 \sqrt[3]{7} \)**.
Answered by
GPT-4o mini
To find the square root of 250, we can simplify it as follows:
\[
\sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \times \sqrt{10} = 5\sqrt{10}
\]
Now, let's look at the provided options:
1. \( 25\sqrt{10} \)
2. \( 250 \)
3. \( 5\sqrt{10} \)
4. \( 10\sqrt{5} \)
The correct answer is **\( 5\sqrt{10} \)**.
\[
\sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \times \sqrt{10} = 5\sqrt{10}
\]
Now, let's look at the provided options:
1. \( 25\sqrt{10} \)
2. \( 250 \)
3. \( 5\sqrt{10} \)
4. \( 10\sqrt{5} \)
The correct answer is **\( 5\sqrt{10} \)**.
Answered by
GPT-4o mini
To find the square root of 128, we can simplify it:
\[
\sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}
\]
Now, let's look at the provided options:
1. \( 8\sqrt{2} \)
2. \( \sqrt{64} \times \sqrt{2} \)
3. \( 4\sqrt{2} \)
4. \( 2\sqrt{4} \)
The correct answer is **\( 8\sqrt{2} \)** and also **\( \sqrt{64} \times \sqrt{2} \)** is another way to express it, but since you asked for the square root of 128, the most straightforward answer is **\( 8\sqrt{2} \)**.
\[
\sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}
\]
Now, let's look at the provided options:
1. \( 8\sqrt{2} \)
2. \( \sqrt{64} \times \sqrt{2} \)
3. \( 4\sqrt{2} \)
4. \( 2\sqrt{4} \)
The correct answer is **\( 8\sqrt{2} \)** and also **\( \sqrt{64} \times \sqrt{2} \)** is another way to express it, but since you asked for the square root of 128, the most straightforward answer is **\( 8\sqrt{2} \)**.