Question

Find the cubic root of 96: √96

Answer 1

To clarify, it seems like you're looking for the cubic root of 96, which is denoted as \( \sqrt[3]{96} \).

To find \( \sqrt[3]{96} \):

1. Factor 96 into its prime factors:
\[
96 = 2^5 \times 3^1
\]

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

- The cubic root of \( 2^5 \) can be simplified:
\[
\sqrt[3]{2^5} = 2^{5/3} = 2^1 \times 2^{2/3} = 2 \times \sqrt[3]{4}
\]

- The cubic root of \( 3^1 \):
\[
\sqrt[3]{3^1} = 3^{1/3}
\]

3. Putting it together:
\[
\sqrt[3]{96} = 2 \times \sqrt[3]{4} \times 3^{1/3}
\]

To approximate the value:
Using a calculator,
\[
\sqrt[3]{96} \approx 4.64
\]

So, the cubic root of 96 is approximately \( 4.64 \).