Question
Identify Roots Quick Check
2 of 52 of 5 Items
Question
Find the cubic root of 96.(1 point)
Responses
2^3√7
2 root index 3 start root 7 end root
2^3√12
2 root index 3 start root 12 end root
2√12
2 start root 12 end root
4√6
4 start root 6 end root
Skip to navigation
Answers
GPT-4o mini
To find the cubic root of 96, we can express 96 in terms of its prime factors and then simplify.
The prime factorization of 96 is:
\( 96 = 2^5 \times 3^1 \)
To find the cubic root (the cube root), we can write:
\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1}
\]
This can be simplified using the property of exponents:
\[
\sqrt[3]{96} = \sqrt[3]{2^3 \times 2^2 \times 3^1} = \sqrt[3]{2^3} \cdot \sqrt[3]{2^2} \cdot \sqrt[3]{3}
\]
Since \( \sqrt[3]{2^3} = 2 \), we have:
\[
\sqrt[3]{96} = 2 \cdot \sqrt[3]{4 \times 3} = 2 \cdot \sqrt[3]{12}
\]
Therefore, the cubic root of 96 is:
\[
2 \sqrt[3]{12}
\]
From the options given, the correct response is:
**2 root index 3 start root 12 end root**
So, the correct answer is:
**2√12** (expressed as cubic root).
The prime factorization of 96 is:
\( 96 = 2^5 \times 3^1 \)
To find the cubic root (the cube root), we can write:
\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1}
\]
This can be simplified using the property of exponents:
\[
\sqrt[3]{96} = \sqrt[3]{2^3 \times 2^2 \times 3^1} = \sqrt[3]{2^3} \cdot \sqrt[3]{2^2} \cdot \sqrt[3]{3}
\]
Since \( \sqrt[3]{2^3} = 2 \), we have:
\[
\sqrt[3]{96} = 2 \cdot \sqrt[3]{4 \times 3} = 2 \cdot \sqrt[3]{12}
\]
Therefore, the cubic root of 96 is:
\[
2 \sqrt[3]{12}
\]
From the options given, the correct response is:
**2 root index 3 start root 12 end root**
So, the correct answer is:
**2√12** (expressed as cubic root).