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Represent perfect squares

A perfect square is a whole number that can be written as the product of a whole number by itself, such as 1=1×11=1\times1, 25=5×525=5\times5, or 100=10×10100=10\times10. It can be represented with equal-row-and-column arrays, as the area of a square, or in exponential form n2n^2; this understanding supports work with factors, exponents, square roots, and area, without extending to irrational roots or advanced algebraic generalizations.

Detailed Explanation: Represent perfect squares

A perfect square is a whole number made by multiplying a whole number by itself:

n2=n×nn^2=n\times n

To represent a perfect square, you can show:

  • equal rows and columns in an array,
  • the area of a square, or
  • exponential form.

Example: Represent 3636.

  1. Find a whole number that multiplies by itself to make 3636:

6×6=366\times6=36

  1. Write it in exponential form:

62=366^2=36

  1. Show it as an array with 66 rows and 66 columns:

□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□\begin{array}{cccccc} \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square \end{array}

  1. Think of the array as a square with side length 66. Its area is:

6×6=366\times6=36

Therefore, 3636 is a perfect square because it can be written as 6×66\times6, or 626^2.

Learn by doing: Represent perfect squares

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    Perfect Squares as Square of Number

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