  # A List of Perfect Squares

Perfect squares are numbers that are created when you take a whole number times itself. They are used in many different topics in algebra, including factoring and radicals, and also in other disciplines like geometry.

 12 = 1 262 = 676 22 = 4 272 = 729 32 = 9 282 = 784 42 = 16 292 = 841 52 = 25 302 = 900 62 = 36 312 = 961 72 = 49 322 = 1024 82 = 64 332 = 1089 92 = 81 342 = 1156 102 = 100 352 = 1225 112 = 121 362 = 1296 122 = 144 372 = 1369 132 = 169 382 = 1444 142 = 196 392 = 1521 152 = 225 402 = 1600 162 = 256 412 = 1681 172 = 289 422 = 1764 182 = 324 432 = 1849 192 = 361 442 = 1936 202 = 400 452 = 2025 212 = 441 462 = 2116 222 = 484 472 = 2209 232 = 529 482 = 2304 242 = 576 492 = 2401 252 = 625 502 = 2500

 Why Are They Called "Perfect Squares?"

Multiplying a number by itself is given this special name because of the geometrical interpretation. Think of the dimensions of a rectangle. If the numbers are not the same, then you will have an imperfect rectangle. But if the dimensions are the same, meaning the length is the same size as the width, then your rectangle will become a square that is perfect.

Take a look at the figure below to get an idea what we are talking about. Notice how when the dimensions are the same it creates a square, but when they are different it creates a rectangle. This is why they are called perfect squares!

What do you think a perfect cube is? Think about the dimensions of a cube vs. the dimensions of a prism (a box).

I bet you figured it out: A perfect cube is something like 33. A short list of perfect cubes are 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.

View more pre algebra math problems or visit the GradeA homepage.

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