To solve the problem of dividing [tex]\( 12 \sqrt[4]{15} \)[/tex] by [tex]\( 8 \sqrt[3]{3} \)[/tex], we need to follow these steps:
1. Calculate the numerator:
- The numerator is given by [tex]\( 12 \sqrt[4]{15} \)[/tex].
- [tex]\( \sqrt[4]{15} \)[/tex] is the fourth root of 15.
2. Calculate the fourth root of 15:
- Numerically, the fourth root of 15 is approximately 1.968300157.
3. Calculate [tex]\( 12 \times \sqrt[4]{15} \)[/tex]:
- Multiplying [tex]\( 12 \)[/tex] by the approximate value of [tex]\( \sqrt[4]{15} \)[/tex]:
[tex]\[
12 \times 1.968300157 \approx 23.615876055185165
\][/tex]
4. Calculate the denominator:
- The denominator is given by [tex]\( 8 \sqrt[3]{3} \)[/tex].
- [tex]\( \sqrt[3]{3} \)[/tex] is the cube root of 3.
5. Calculate the cube root of 3:
- Numerically, the cube root of 3 is approximately 1.442249570.
6. Calculate [tex]\( 8 \times \sqrt[3]{3} \)[/tex]:
- Multiplying [tex]\( 8 \)[/tex] by the approximate value of [tex]\( \sqrt[3]{3} \)[/tex]:
[tex]\[
8 \times 1.442249570 \approx 11.537996562459266
\][/tex]
7. Divide the numerator by the denominator:
- To find the result, we divide [tex]\( 23.615876055185165 \)[/tex] by [tex]\( 11.537996562459266 \)[/tex]:
[tex]\[
\frac{23.615876055185165}{11.537996562459266} \approx 2.0467917395662285
\][/tex]
So, the result of dividing [tex]\( 12 \sqrt[4]{15} \)[/tex] by [tex]\( 8 \sqrt[3]{3} \)[/tex] is approximately [tex]\( 2.0467917395662285 \)[/tex].
To summarize:
1. Numerator: [tex]\( 12 \sqrt[4]{15} \approx 23.615876055185165 \)[/tex]
2. Denominator: [tex]\( 8 \sqrt[3]{3} \approx 11.537996562459266 \)[/tex]
3. Final Result: [tex]\( \frac{12 \sqrt[4]{15}}{8 \sqrt[3]{3}} \approx 2.0467917395662285 \)[/tex]
