Part A
Complete the table by squaring each positive [tex]$x$[/tex]-value listed.
Answer (2)
Calculate the square of 2: 2 2 = 4 .
Calculate the square of 3: 3 2 = 9 .
Calculate the square of 4: 4 2 = 16 .
Calculate the square of 5: 5 2 = 25 .
Calculate the square of 6: 6 2 = 36 .
Calculate the square of 7: 7 2 = 49 .
Calculate the square of 8: 8 2 = 64 .
Calculate the square of 9: 9 2 = 81 .
Calculate the square of 10: 1 0 2 = 100 .
Correct the table entry for x = 10 : 100 .
Explanation
Understanding the Problem We are given a table with x values and asked to complete the table by finding the square of each x value. This means we need to calculate x 2 for each given x .
Calculating 2 2 For x = 2 , we calculate x 2 = 2 2 = 2 × 2 = 4 .
Calculating 3 2 For x = 3 , we calculate x 2 = 3 2 = 3 × 3 = 9 .
Calculating 4 2 For x = 4 , we calculate x 2 = 4 2 = 4 × 4 = 16 .
Calculating 5 2 For x = 5 , we calculate x 2 = 5 2 = 5 × 5 = 25 .
Calculating 6 2 For x = 6 , we calculate x 2 = 6 2 = 6 × 6 = 36 .
Calculating 7 2 For x = 7 , we calculate x 2 = 7 2 = 7 × 7 = 49 .
Calculating 8 2 For x = 8 , we calculate x 2 = 8 2 = 8 × 8 = 64 .
Calculating 9 2 For x = 9 , we calculate x 2 = 9 2 = 9 × 9 = 81 .
Calculating 1 0 2 For x = 10 , we calculate x 2 = 1 0 2 = 10 × 10 = 100 . The table incorrectly shows 11, so we correct it to 100.
Examples
Understanding squares is fundamental in many areas, such as calculating the area of a square. For example, if you're designing a square garden that is 5 meters on each side, you need to calculate 5 2 to find the area, which is 25 square meters. This concept extends to more complex calculations in engineering, physics, and even financial modeling, where understanding exponential growth or decay is crucial.
To complete the table, we calculated the square of each positive x-value. Squaring a number involves multiplying it by itself. For instance, 1 0 2 = 100 correctly represents the square of 10.
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