What is a perfect square? How do you know if a number is a perfect square?

In this article, we’ll define perfect squares, provide a list of the first 25 perfect squares (and the integers that make them up), and teach you how to tell if a number is a perfect square.

##
What Is a Perfect Square?

A perfect square is a number that can be expressed as the product of two equal integers.

What does that mean?

Basically, a perfect square is what you get when you multiply two equal integers by each other.

For instance:

$$5 * 5 = 25$$

25 is a perfect square because you’re multiplying two equal integers (5 and 5) by each other.

You can also express $5 * 5$ as $5^2$. That’s where you get the term “perfect square”

##
List of Perfect Squares

Here’s a list of the first 25 perfect squares. A hint: if you want to create a perfect square, simply square an integer!

Square |
Integers |

1 | $1 * 1$ |

4 | $2 * 2$ |

9 | $3 * 3$ |

16 | $4 * 4$ |

25 | $5 * 5$ |

36 | $6 * 6$ |

49 | $7 * 7$ |

64 | $8 * 8$ |

81 | $9 * 9$ |

100 | $10 * 10$ |

121 | $11 * 11$ |

144 | $12 * 12$ |

169 | $13 * 13$ |

196 | $14 * 14$ |

225 | $15 * 15$ |

256 | $16 * 16$ |

289 | $17 * 17$ |

324 | $18 * 18$ |

361 | $19 * 19$ |

400 | $20 * 20$ |

441 | $21 * 21$ |

484 | $22 * 22$ |

529 | $23 * 23$ |

576 | $24 * 24$ |

625 | $25 * 25$ |

##
How to Tell If a Number Is a Perfect Square

You can tell if a number is a perfect square in a couple of different ways.

First of all, if you create a square by multiplying two equal integers by each other, then the product is a perfect square.

So, $1 * 1$ is a perfect square. So is $10 * 10$ and $1,000 * 1,000$.

You can also tell if a number is a perfect square by finding its square roots.

Finding the square root is the inverse (opposite) of squaring a number.

If you find the square root of a number and it’s a whole integer, that tells you that the number is a perfect square.

For instance, the square root of 25 is 5. The square root of 26 is not a whole integer. So, 26 is not a perfect square.

##
Key Takeaways: Understanding Perfect Squares

A perfect square is a number that can be expressed as the product of two equal integers.

You can tell if a number by finding its square root and seeing if that square root is a whole integer.

##
What’s Next?

Getting ready to take the ACT?

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Taking the SAT instead?

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Looking to brush up on your fundamental algebra skills?

A good place to start is mastering systems of equations.