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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"

Respuesta :

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 [tex]1^2 = 1[/tex]
  • 4 as a base raised to the second power is [tex]2^2 = 4[/tex]
  • 9 as a base raised to the second power is [tex]3^2 = 9[/tex]
  • 16 as a base raised to the second power is [tex]4^2 = 16[/tex]
  • 25 as a base raised to the second power is [tex]5^2 = 25[/tex]
  • 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:

[tex]x = \sqrt{x}^2[/tex]

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1, 4, 9, 16, and 25

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

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

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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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