Question

Find the square root of 96.(1 point)
Responses

64–√
6 start root 4 end root

24
24

46–√
4 start root 6 end root

166–√

Answer 1

Find the cubic root of 96.(1 point)
Responses

212−−√
2 start root 12 end root

27–√3
2 root index 3 start root 7 end root

212−−√3
2 root index 3 start root 12 end root

46–√

Answer 2

Find the cubic root of 189.(1 point)
Responses

37–√3
3 root index 3 start root 7 end root

277–√3
27 root index 3 start root 7 end root

37–√
3 start root 7 end root

921−−√3

Answer 3

Find the square root of 250.(1 point)
Responses

105–√
10 start root 5 end root

250
250

2510−−√
25 start root 10 end root

510−−√

Answer 4

Find the square root of 128.(1 point)
Responses

24–√
2 start root 4 end root

64 −−−√ x 2–√
start root 64 end root x start root 2 end root

82–√
8 start root 2 end root

42–√

Answer 5

To find the square root of 96, we can simplify it first.

We can factor 96 into its prime factors:
\[ 96 = 16 \times 6 = 4^2 \times 6. \]

Now, we can take the square root:
\[ \sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}. \]

So, the square root of 96 is:
\[ 4\sqrt{6}. \]

Among the provided responses, the correct answer is:
**4 start root 6 end root.**

Answer 6

To find the cubic root of 96, we can simplify it, although cubic roots can be a bit more straightforward depending on the factors.

The prime factorization of 96 is:
\[ 96 = 2^5 \times 3^1. \]

To find the cubic root, we can apply the property of indices:
\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} = \sqrt[3]{2^5} \times \sqrt[3]{3^1} = 2^{5/3} \times 3^{1/3}.
\]

Now, let’s simplify \(2^{5/3}\):
\[
2^{5/3} = 2^{1 + 2/3} = 2^1 \times 2^{2/3} = 2 \times \sqrt[3]{4}.
\]

Therefore, we can express the cubic root of 96 as:
\[
\sqrt[3]{96} = 2 \times \sqrt[3]{4} \times \sqrt[3]{3} = 2 \times \sqrt[3]{12}.
\]

Thus, the cubic root of 96 is:
\[
2\sqrt[3]{12}.
\]

Among the provided responses, the correct answer is:
**2 root index 3 start root 12 end root.**

Answer 7

To find the cubic root of 189, we first perform its prime factorization:

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

Now we can find the cubic root:

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

Thus, the cubic root of 189 is:

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

Among the provided responses, the correct answer is:

**3 start root 7 end root.**

Answer 8

To find the square root of 250, we can simplify it first.

The prime factorization of 250 is:
\[ 250 = 25 \times 10 = 5^2 \times 10. \]

Now, we can take the square root:
\[ \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \times \sqrt{10} = 5 \sqrt{10}. \]

So, the square root of 250 is:
\[ 5\sqrt{10}. \]

Among the provided responses, the correct answer is:
**5 start root 10 end root.**

Answer 9

To find the square root of 128, let's start with simplifying it.

1. **Factor 128**:
\[
128 = 64 \times 2 = 8^2 \times 2 = 4^2 \times 8 = 2^7
\]

2. **Take the square root**:
\[
\sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}
\]

So, the square root of 128 is:
\[
8\sqrt{2}
\]

Among the provided responses, the correct answer is:
**8 start root 2 end root.**