Question

drag each value to the correct location on the table.

identify whether the given numbers are perfect squares, perfect cubes, or neither.

perfect square | perfect cube | neither

values to drag: 8, 9, 21, 27, 1,331, 1,332, 100, 1,000, 126, 125, 25, 81

Explanation:

Define perfect squares and perfect cubes

Using the Exponent Rules knowledge point
An integer \(n\) is a perfect square if \(n = k^2\) for some integer \(k\).
An integer \(n\) is a perfect cube if \(n = m^3\) for some integer \(m\).

Analyze each given number

We evaluate each number from the list: \(8, 9, 21, 27, 1331, 1332, 100, 1000, 126, 125, 25, 81\).

• \(8 = 2^3\) (Perfect Cube)
• \(9 = 3^2\) (Perfect Square)
• \(21\) (Neither)
• \(27 = 3^3\) (Perfect Cube)
• \(1331 = 11^3\) (Perfect Cube)
• \(1332\) (Neither)
• \(100 = 10^2\) (Perfect Square)
• \(1000 = 10^3\) (Perfect Cube)
• \(126\) (Neither)
• \(125 = 5^3\) (Perfect Cube)
• \(25 = 5^2\) (Perfect Square)
• \(81 = 9^2\) (Perfect Square)

Group the numbers into categories

• Perfect Square: \(9, 25, 81, 100\)
• Perfect Cube: \(8, 27, 125, 1000, 1331\)
• Neither: \(21, 126, 1332\)

Answer:

Perfect Square	Perfect Cube	Neither