To solve the given problem, let's examine each of the provided expressions one by one:
Option 1: [tex]\( \frac{5 \sqrt{7}}{7} \)[/tex]
1. The numerator is [tex]\(5 \sqrt{7}\)[/tex].
2. The denominator is 7.
3. Divide the numerator by the denominator: [tex]\( \frac{5 \sqrt{7}}{7} \)[/tex].
Calculating this value:
[tex]\[ \frac{5 \sqrt{7}}{7} = 1.889822365046136 \][/tex]
Option 2: [tex]\( \frac{3 \sqrt{7}}{7} \)[/tex]
1. The numerator is [tex]\(3 \sqrt{7}\)[/tex].
2. The denominator is 7.
3. Divide the numerator by the denominator: [tex]\( \frac{3 \sqrt{7}}{7} \)[/tex].
Calculating this value:
[tex]\[ \frac{3 \sqrt{7}}{7} = 1.1338934190276817 \][/tex]
Option 3: [tex]\( \frac{-5 \sqrt{7}}{7} \)[/tex]
1. The numerator is [tex]\(-5 \sqrt{7}\)[/tex].
2. The denominator is 7.
3. Divide the numerator by the denominator: [tex]\( \frac{-5 \sqrt{7}}{7} \)[/tex].
Calculating this value:
[tex]\[ \frac{-5 \sqrt{7}}{7} = -1.889822365046136 \][/tex]
Therefore, the detailed step-by-step numerical solutions for the given expressions are:
1. [tex]\( \frac{5 \sqrt{7}}{7} = 1.889822365046136 \)[/tex]
2. [tex]\( \frac{3 \sqrt{7}}{7} = 1.1338934190276817 \)[/tex]
3. [tex]\( \frac{-5 \sqrt{7}}{7} = -1.889822365046136 \)[/tex]
