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Sagot :
To solve the given problems involving the addition of square roots in a step-by-step manner, let's work on each row of the table individually:
### First Row Calculation: [tex]\( 2 \sqrt{3} + 6 \sqrt{3} \)[/tex]
We need to add two terms involving [tex]\( \sqrt{3} \)[/tex].
1. Write the expression: [tex]\( 2 \sqrt{3} + 6 \sqrt{3} \)[/tex].
2. Factor out the common term [tex]\( \sqrt{3} \)[/tex]:
[tex]\[ 2 \sqrt{3} + 6 \sqrt{3} = (2 + 6) \sqrt{3} \][/tex]
3. Perform the addition inside the parentheses:
[tex]\[ (2 + 6) \sqrt{3} = 8 \sqrt{3} \][/tex]
4. The simplified result is [tex]\( 8 \sqrt{3} \)[/tex].
Thus, the first row fills in as:
[tex]\[ \begin{array}{|c|c|c|} \hline Penjumlahan \text{ Bentuk Akar} & \text{Bentuk Panjang} & \text{Kesimpulan} \\ \hline 2 \sqrt{3} + 6 \sqrt{3} & (2+6)\sqrt{3} & 8 \sqrt{3} \\ \hline \end{array} \][/tex]
### Second Row Calculation: [tex]\( 7 \sqrt{5} + 8 \sqrt{5} \)[/tex]
We need to add two terms involving [tex]\( \sqrt{5} \)[/tex].
1. Write the expression: [tex]\( 7 \sqrt{5} + 8 \sqrt{5} \)[/tex].
2. Factor out the common term [tex]\( \sqrt{5} \)[/tex]:
[tex]\[ 7 \sqrt{5} + 8 \sqrt{5} = (7 + 8) \sqrt{5} \][/tex]
3. Perform the addition inside the parentheses:
[tex]\[ (7 + 8) \sqrt{5} = 15 \sqrt{5} \][/tex]
4. The simplified result is [tex]\( 15 \sqrt{5} \)[/tex].
Thus, the second row fills in as:
[tex]\[ \begin{array}{|c|c|c|} \hline Penjumlahan \text{ Bentuk Akar} & \text{Bentuk Panjang} & \text{Kesimpulan} \\ \hline 2 \sqrt{3} + 6 \sqrt{3} & (2+6)\sqrt{3} & 8 \sqrt{3} \\ \hline 7 \sqrt{5} + 8 \sqrt{5} & (7+8)\sqrt{5} & 15 \sqrt{5} \\ \hline \end{array} \][/tex]
### Third Row Calculation: Combining Terms Involving [tex]\( \sqrt{10} \)[/tex]
1. Write the expression where you combine the coefficients inside parentheses:
[tex]\[ (9 - 3 + 6) \sqrt{10} \][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[ 9 - 3 + 6 = 12 \][/tex]
3. The simplified result is:
[tex]\[ 12 \sqrt{10} \][/tex]
Thus, the third row fills in as:
[tex]\[ \begin{array}{|c|c|c|} \hline Penjumlahan \text{ Bentuk Akar} & \text{Bentuk Panjang} & \text{Kesimpulan} \\ \hline 2 \sqrt{3} + 6 \sqrt{3} & (2+6)\sqrt{3} & 8 \sqrt{3} \\ \hline 7 \sqrt{5} + 8 \sqrt{5} & (7+8)\sqrt{5} & 15 \sqrt{5} \\ \hline \text{Combining terms with}\, \sqrt{10} & (9-3+6)\sqrt{10} & 12\sqrt{10} \\ \hline \end{array} \][/tex]
Thus completing the entire table, all rows fill in as:
[tex]\[ \begin{array}{|c|c|c|} \hline Penjumlahan \text{ Bentuk Akar} & \text{Bentuk Panjang} & \text{Kesimpulan} \\ \hline 2 \sqrt{3} + 6 \sqrt{3} & (2+6)\sqrt{3} & 8 \sqrt{3} \\ \hline 7 \sqrt{5} + 8 \sqrt{5} & (7+8)\sqrt{5} & 15 \sqrt{5} \\ \hline \text{Combining terms with}\, \sqrt{10} & (9-3+6)\sqrt{10} & 12\sqrt{10} \\ \hline \end{array} \][/tex]
### First Row Calculation: [tex]\( 2 \sqrt{3} + 6 \sqrt{3} \)[/tex]
We need to add two terms involving [tex]\( \sqrt{3} \)[/tex].
1. Write the expression: [tex]\( 2 \sqrt{3} + 6 \sqrt{3} \)[/tex].
2. Factor out the common term [tex]\( \sqrt{3} \)[/tex]:
[tex]\[ 2 \sqrt{3} + 6 \sqrt{3} = (2 + 6) \sqrt{3} \][/tex]
3. Perform the addition inside the parentheses:
[tex]\[ (2 + 6) \sqrt{3} = 8 \sqrt{3} \][/tex]
4. The simplified result is [tex]\( 8 \sqrt{3} \)[/tex].
Thus, the first row fills in as:
[tex]\[ \begin{array}{|c|c|c|} \hline Penjumlahan \text{ Bentuk Akar} & \text{Bentuk Panjang} & \text{Kesimpulan} \\ \hline 2 \sqrt{3} + 6 \sqrt{3} & (2+6)\sqrt{3} & 8 \sqrt{3} \\ \hline \end{array} \][/tex]
### Second Row Calculation: [tex]\( 7 \sqrt{5} + 8 \sqrt{5} \)[/tex]
We need to add two terms involving [tex]\( \sqrt{5} \)[/tex].
1. Write the expression: [tex]\( 7 \sqrt{5} + 8 \sqrt{5} \)[/tex].
2. Factor out the common term [tex]\( \sqrt{5} \)[/tex]:
[tex]\[ 7 \sqrt{5} + 8 \sqrt{5} = (7 + 8) \sqrt{5} \][/tex]
3. Perform the addition inside the parentheses:
[tex]\[ (7 + 8) \sqrt{5} = 15 \sqrt{5} \][/tex]
4. The simplified result is [tex]\( 15 \sqrt{5} \)[/tex].
Thus, the second row fills in as:
[tex]\[ \begin{array}{|c|c|c|} \hline Penjumlahan \text{ Bentuk Akar} & \text{Bentuk Panjang} & \text{Kesimpulan} \\ \hline 2 \sqrt{3} + 6 \sqrt{3} & (2+6)\sqrt{3} & 8 \sqrt{3} \\ \hline 7 \sqrt{5} + 8 \sqrt{5} & (7+8)\sqrt{5} & 15 \sqrt{5} \\ \hline \end{array} \][/tex]
### Third Row Calculation: Combining Terms Involving [tex]\( \sqrt{10} \)[/tex]
1. Write the expression where you combine the coefficients inside parentheses:
[tex]\[ (9 - 3 + 6) \sqrt{10} \][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[ 9 - 3 + 6 = 12 \][/tex]
3. The simplified result is:
[tex]\[ 12 \sqrt{10} \][/tex]
Thus, the third row fills in as:
[tex]\[ \begin{array}{|c|c|c|} \hline Penjumlahan \text{ Bentuk Akar} & \text{Bentuk Panjang} & \text{Kesimpulan} \\ \hline 2 \sqrt{3} + 6 \sqrt{3} & (2+6)\sqrt{3} & 8 \sqrt{3} \\ \hline 7 \sqrt{5} + 8 \sqrt{5} & (7+8)\sqrt{5} & 15 \sqrt{5} \\ \hline \text{Combining terms with}\, \sqrt{10} & (9-3+6)\sqrt{10} & 12\sqrt{10} \\ \hline \end{array} \][/tex]
Thus completing the entire table, all rows fill in as:
[tex]\[ \begin{array}{|c|c|c|} \hline Penjumlahan \text{ Bentuk Akar} & \text{Bentuk Panjang} & \text{Kesimpulan} \\ \hline 2 \sqrt{3} + 6 \sqrt{3} & (2+6)\sqrt{3} & 8 \sqrt{3} \\ \hline 7 \sqrt{5} + 8 \sqrt{5} & (7+8)\sqrt{5} & 15 \sqrt{5} \\ \hline \text{Combining terms with}\, \sqrt{10} & (9-3+6)\sqrt{10} & 12\sqrt{10} \\ \hline \end{array} \][/tex]
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