To determine which expression is equivalent to [tex]\( 24^{\frac{1}{3}} \)[/tex], let's evaluate the given expressions step by step and compare each with [tex]\( 24^{\frac{1}{3}} \)[/tex].
First, we calculate [tex]\( 24^{\frac{1}{3}} \)[/tex]:
[tex]\[ 24^{\frac{1}{3}} \approx 2.8844991406148166 \][/tex]
Now let's evaluate each given expression:
1. [tex]\( 2\sqrt{3} \)[/tex]:
[tex]\[ 2\sqrt{3} \approx 2 \times 1.7320508075688772 \approx 3.4641016151377544 \][/tex]
2. [tex]\( 2\sqrt[3]{3} \)[/tex]:
[tex]\[ 2\sqrt[3]{3} \approx 2 \times 1.4422495703074083 \approx 2.8844991406148166 \][/tex]
3. [tex]\( 2\sqrt{6} \)[/tex]:
[tex]\[ 2\sqrt{6} \approx 2 \times 2.449489742783178 \approx 4.898979485566356 \][/tex]
4. [tex]\( 2\sqrt[3]{6} \)[/tex]:
[tex]\[ 2\sqrt[3]{6} \approx 2 \times 1.8171205928321397 \approx 3.6342411856642793 \][/tex]
Upon comparing the results:
- [tex]\( 2 \sqrt{3} \approx 3.4641016151377544 \)[/tex]
- [tex]\( 2 \sqrt[3]{3} \approx 2.8844991406148166 \)[/tex]
- [tex]\( 2 \sqrt{6} \approx 4.898979485566356 \)[/tex]
- [tex]\( 2 \sqrt[3]{6} \approx 3.6342411856642793 \)[/tex]
We notice that:
[tex]\[ 24^{\frac{1}{3}} \approx 2.8844991406148166 \][/tex]
Thus, the expression [tex]\( 2 \sqrt[3]{3} \approx 2.8844991406148166 \)[/tex] is equivalent to [tex]\( 24^{\frac{1}{3}} \)[/tex].
So, the correct answer is:
[tex]\[ 2 \sqrt[3]{3} \][/tex]
