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Write each of the numbers 1, 4, 9, 16, and 25 as a base raised to the second power. Explain why these numbers are sometimes called "perfect squares"

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leahboris321

First, we can raise each number to the second power by multipying it by itself. :)
1^2=1
4^2=16
9^2=81
16^2=256

These numbers are called "perfect squares" because their square roots are whole numbers, rather than decimals. For example, If you had a square with an area of 16, the side legnths of the square would be the whole (thus "perfect") number 4. For this reason, 16 (4^2) is considered a "perfect square" number. I hope that makes sense!! :)

  • 1 as a base raised to the second power is \(1^2 = 1\)
  • 4 as a base raised to the second power is \(2^2 = 4\)
  • 9 as a base raised to the second power is \(3^2 = 9\)
  • 16 as a base raised to the second power is \(4^2 = 16\)
  • 25 as a base raised to the second power is \(5^2 = 25\)
  • They are perfect squares because their square roots are whole numbers.

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A number x as a base raised to the second power is written as:

\(x = \sqrt{x}^2\)

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1, 4, 9, 16, and 25

We find the square root of each of these numbers, so:

  • Since \(\sqrt{1} = 1\), 1 as a base raised to the second power is \(1^2 = 1\).
  • Since \(\sqrt{4} = 2\), 4 as a base raised to the second power is \(2^2 = 4\)
  • Since \(\sqrt{9} = 3\), 9 as a base raised to the second power is \(3^2 = 9\)
  • Since \(\sqrt{16} = 4\), 16 as a base raised to the second power is \(4^2 = 16\)
  • Since \(\sqrt{26} = 2\), 25 as a base raised to the second power is \(5^2 = 25\)

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Each number that has a whole square root is called perfect square, which is the case for 1, 4, 9, 16, and 25.

A similar question is found at https://brainly.com/question/2675310

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