Let's solve the given mathematical expression step-by-step:
The expression given is:
[tex]\[ \sqrt[3]{54} + \sqrt[3]{250} - \frac{3}{4} \sqrt{\frac{32}{25}} \][/tex]
1. Calculate [tex]\( \sqrt[3]{54} \)[/tex]:
We need to find the cube root of 54:
[tex]\[ \sqrt[3]{54} \approx 3.7798 \][/tex]
2. Calculate [tex]\( \sqrt[3]{250} \)[/tex]:
Next, we find the cube root of 250:
[tex]\[ \sqrt[3]{250} \approx 6.2996 \][/tex]
3. Simplify and calculate [tex]\( \frac{3}{4} \sqrt{\frac{32}{25}} \)[/tex]:
First, simplify the fraction inside the square root:
[tex]\[ \frac{32}{25} = 1.28 \][/tex]
Now find the square root of 1.28:
[tex]\[ \sqrt{1.28} \approx 1.1314 \][/tex]
Then multiply by [tex]\( \frac{3}{4} \)[/tex] to get:
[tex]\[ \frac{3}{4} \times 1.1314 \approx 0.8485 \][/tex]
4. Combine the results:
Finally, we need to add the results from steps 1 and 2, and then subtract the result from step 3:
[tex]\[ 3.7798 + 6.2996 - 0.8485 \approx 9.2308 \][/tex]
So, the final result of the given expression is:
[tex]\[ \sqrt[3]{54} + \sqrt[3]{250} - \frac{3}{4} \sqrt{\frac{32}{25}} \approx 9.2308 \][/tex]
