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Sagot :
Alright, let's carefully go through the mathematical expressions given under the "Tiles" and "Pairs" sections. For each expression, we'll find its numerical value.
### Tiles Section:
1. [tex]\(3 \sqrt[4]{50}\)[/tex]
2. [tex]\(42 \sqrt{2}\)[/tex]
3. [tex]\(4 \sqrt[3]{7}\)[/tex]
4. [tex]\(4 \sqrt[5]{3}\)[/tex]
5. [tex]\(3 \sqrt[5]{4}\)[/tex]
6. [tex]\(7 \sqrt[4]{38}\)[/tex]
#### Calculated Values:
1. [tex]\(3 \sqrt[4]{50} \approx 7.977443845417483\)[/tex]
2. [tex]\(42 \sqrt{2} \approx 59.396969619669996\)[/tex]
3. [tex]\(4 \sqrt[3]{7} \approx 7.651724731089556\)[/tex]
4. [tex]\(4 \sqrt[5]{3} \approx 4.98292375846207\)[/tex]
5. [tex]\(3 \sqrt[5]{4} \approx 3.9585237323186826\)[/tex]
6. [tex]\(7 \sqrt[4]{38} \approx 17.379766573388718\)[/tex]
### Pairs Section:
Let's compute the values given in this section to match the calculated values from the Tiles section.
1. No value is provided and hence it remains as unspecified.
2. [tex]\(448^{\frac{1}{3}} \approx 7.651724731089556\)[/tex] - This matches the value computed as [tex]\(4 \sqrt[3]{7}\)[/tex] from the Tiles section.
3. [tex]\(3,528^{\frac{1}{2}} \approx 59.39696961966999\)[/tex] - This matches the value of [tex]\(42 \sqrt{2}\)[/tex].
4. [tex]\(4,050^{\frac{1}{4}} \approx 7.977443845417483\)[/tex] - This matches the value of [tex]\(3 \sqrt[4]{50}\)[/tex].
### Detailed Results:
Based on the calculated values, the detailed pairs can be defined as:
For the given pairs:
- [tex]\(\square \longrightarrow\)[/tex] remains unspecified and is left unspecified in the answer.
- [tex]\(448^{\frac{1}{3}} \longrightarrow 4 \sqrt[3]{7} = 7.651724731089556\)[/tex].
- [tex]\(3,528^{\frac{1}{2}} \longrightarrow 42 \sqrt{2} = 59.396969619669996\)[/tex].
- [tex]\(4,050^{\frac{1}{4}} \longrightarrow 3 \sqrt[4]{50} = 7.977443845417483\)[/tex].
Hence, the final values would look something like this:
- Unspecified: corresponds to no given value.
The final result in pairings as per the questions' numerical examples given would be:
- No value: [tex]\(None\)[/tex]
- [tex]\(448^{\frac{1}{3}} \longrightarrow 7.651724731089556 \)[/tex]
- [tex]\(3,528^{\frac{1}{2}} \longrightarrow 59.396969619669996 \)[/tex]
- [tex]\(4,050^{\frac{1}{4}} \longrightarrow 7.977443845417483 \)[/tex]
Thus, the pairing values extracted from the calculations are:
[tex]\[ ((7.977443845417483, 59.396969619669996, 7.651724731089556, 4.98292375846207, 3.9585237323186826, 17.379766573388718), (None, 7.651724731089556, 59.39696961966999, 7.977443845417483)) \][/tex]
### Tiles Section:
1. [tex]\(3 \sqrt[4]{50}\)[/tex]
2. [tex]\(42 \sqrt{2}\)[/tex]
3. [tex]\(4 \sqrt[3]{7}\)[/tex]
4. [tex]\(4 \sqrt[5]{3}\)[/tex]
5. [tex]\(3 \sqrt[5]{4}\)[/tex]
6. [tex]\(7 \sqrt[4]{38}\)[/tex]
#### Calculated Values:
1. [tex]\(3 \sqrt[4]{50} \approx 7.977443845417483\)[/tex]
2. [tex]\(42 \sqrt{2} \approx 59.396969619669996\)[/tex]
3. [tex]\(4 \sqrt[3]{7} \approx 7.651724731089556\)[/tex]
4. [tex]\(4 \sqrt[5]{3} \approx 4.98292375846207\)[/tex]
5. [tex]\(3 \sqrt[5]{4} \approx 3.9585237323186826\)[/tex]
6. [tex]\(7 \sqrt[4]{38} \approx 17.379766573388718\)[/tex]
### Pairs Section:
Let's compute the values given in this section to match the calculated values from the Tiles section.
1. No value is provided and hence it remains as unspecified.
2. [tex]\(448^{\frac{1}{3}} \approx 7.651724731089556\)[/tex] - This matches the value computed as [tex]\(4 \sqrt[3]{7}\)[/tex] from the Tiles section.
3. [tex]\(3,528^{\frac{1}{2}} \approx 59.39696961966999\)[/tex] - This matches the value of [tex]\(42 \sqrt{2}\)[/tex].
4. [tex]\(4,050^{\frac{1}{4}} \approx 7.977443845417483\)[/tex] - This matches the value of [tex]\(3 \sqrt[4]{50}\)[/tex].
### Detailed Results:
Based on the calculated values, the detailed pairs can be defined as:
For the given pairs:
- [tex]\(\square \longrightarrow\)[/tex] remains unspecified and is left unspecified in the answer.
- [tex]\(448^{\frac{1}{3}} \longrightarrow 4 \sqrt[3]{7} = 7.651724731089556\)[/tex].
- [tex]\(3,528^{\frac{1}{2}} \longrightarrow 42 \sqrt{2} = 59.396969619669996\)[/tex].
- [tex]\(4,050^{\frac{1}{4}} \longrightarrow 3 \sqrt[4]{50} = 7.977443845417483\)[/tex].
Hence, the final values would look something like this:
- Unspecified: corresponds to no given value.
The final result in pairings as per the questions' numerical examples given would be:
- No value: [tex]\(None\)[/tex]
- [tex]\(448^{\frac{1}{3}} \longrightarrow 7.651724731089556 \)[/tex]
- [tex]\(3,528^{\frac{1}{2}} \longrightarrow 59.396969619669996 \)[/tex]
- [tex]\(4,050^{\frac{1}{4}} \longrightarrow 7.977443845417483 \)[/tex]
Thus, the pairing values extracted from the calculations are:
[tex]\[ ((7.977443845417483, 59.396969619669996, 7.651724731089556, 4.98292375846207, 3.9585237323186826, 17.379766573388718), (None, 7.651724731089556, 59.39696961966999, 7.977443845417483)) \][/tex]
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