Answer :
Certainly! Let's break the problem into two parts and solve each one step-by-step to ensure clarity.
### Part 1: Evaluate the Expression
Evaluate the expression [tex]\(\sqrt[3]{95} + 4 \sqrt{63} - 2 \sqrt{28}\)[/tex].
1. Cube Root of 95
[tex]\[ \sqrt[3]{95} \approx 4.562902635386966 \][/tex]
2. Four Times the Square Root of 63
[tex]\[ 4 \sqrt{63} \approx 4 \times 7.937253933193772 = 31.74901573277509 \][/tex]
3. Twice the Square Root of 28
[tex]\[ 2 \sqrt{28} \approx 2 \times 5.291502622129181 = 10.583005244258363 \][/tex]
4. Now Combine the Results
[tex]\[ \sqrt[3]{95} + 4 \sqrt{63} - 2 \sqrt{28} \approx 4.562902635386966 + 31.74901573277509 - 10.583005244258363 = 25.72891312390369 \][/tex]
### Part 2: Simplify the Expression
Simplify the expression [tex]\(\frac{21}{44} \left(\frac{3}{21} + y^3\right)\)[/tex].
1. Simplify Inside the Parentheses
[tex]\[ \frac{3}{21} = \frac{1}{7} \][/tex]
So, the expression inside the parentheses becomes:
[tex]\[ \frac{1}{7} + y^3 \][/tex]
2. Multiply by [tex]\(\frac{21}{44}\)[/tex]
[tex]\[ \frac{21}{44} \left(\frac{1}{7} + y^3\right) \][/tex]
3. Distribute the [tex]\(\frac{21}{44}\)[/tex]
[tex]\[ \frac{21}{44} \times \frac{1}{7} + \frac{21}{44} \times y^3 \][/tex]
Simplify each term:
[tex]\[ \frac{21}{44} \times \frac{1}{7} = \frac{21}{308} = \frac{21}{308} = \frac{3}{44} \approx 0.0681818181818182 \][/tex]
[tex]\[ \frac{21}{44} \times y^3 = \frac{21}{44} y^3 \approx 0.477272727272727 y^3 \][/tex]
So the simplified expression is:
[tex]\[ \frac{3}{44} + \frac{21}{44} y^3 \approx 0.0681818181818182 + 0.477272727272727 y^3 \][/tex]
### Final Results:
1. The evaluated expression:
[tex]\[ \sqrt[3]{95} + 4 \sqrt{63} - 2 \sqrt{28} \approx 25.72891312390369 \][/tex]
2. The simplified expression:
[tex]\[ \frac{21}{44} \left(\frac{3}{21} + y^3\right) \approx 0.477272727272727 y^3 + 0.0681818181818182 \][/tex]
### Part 1: Evaluate the Expression
Evaluate the expression [tex]\(\sqrt[3]{95} + 4 \sqrt{63} - 2 \sqrt{28}\)[/tex].
1. Cube Root of 95
[tex]\[ \sqrt[3]{95} \approx 4.562902635386966 \][/tex]
2. Four Times the Square Root of 63
[tex]\[ 4 \sqrt{63} \approx 4 \times 7.937253933193772 = 31.74901573277509 \][/tex]
3. Twice the Square Root of 28
[tex]\[ 2 \sqrt{28} \approx 2 \times 5.291502622129181 = 10.583005244258363 \][/tex]
4. Now Combine the Results
[tex]\[ \sqrt[3]{95} + 4 \sqrt{63} - 2 \sqrt{28} \approx 4.562902635386966 + 31.74901573277509 - 10.583005244258363 = 25.72891312390369 \][/tex]
### Part 2: Simplify the Expression
Simplify the expression [tex]\(\frac{21}{44} \left(\frac{3}{21} + y^3\right)\)[/tex].
1. Simplify Inside the Parentheses
[tex]\[ \frac{3}{21} = \frac{1}{7} \][/tex]
So, the expression inside the parentheses becomes:
[tex]\[ \frac{1}{7} + y^3 \][/tex]
2. Multiply by [tex]\(\frac{21}{44}\)[/tex]
[tex]\[ \frac{21}{44} \left(\frac{1}{7} + y^3\right) \][/tex]
3. Distribute the [tex]\(\frac{21}{44}\)[/tex]
[tex]\[ \frac{21}{44} \times \frac{1}{7} + \frac{21}{44} \times y^3 \][/tex]
Simplify each term:
[tex]\[ \frac{21}{44} \times \frac{1}{7} = \frac{21}{308} = \frac{21}{308} = \frac{3}{44} \approx 0.0681818181818182 \][/tex]
[tex]\[ \frac{21}{44} \times y^3 = \frac{21}{44} y^3 \approx 0.477272727272727 y^3 \][/tex]
So the simplified expression is:
[tex]\[ \frac{3}{44} + \frac{21}{44} y^3 \approx 0.0681818181818182 + 0.477272727272727 y^3 \][/tex]
### Final Results:
1. The evaluated expression:
[tex]\[ \sqrt[3]{95} + 4 \sqrt{63} - 2 \sqrt{28} \approx 25.72891312390369 \][/tex]
2. The simplified expression:
[tex]\[ \frac{21}{44} \left(\frac{3}{21} + y^3\right) \approx 0.477272727272727 y^3 + 0.0681818181818182 \][/tex]
