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Powers are used to represent the repeated multiplication of a number by itself. When the exponent of a power is two, the value of the power is a perfect square. Perfect squares are a particular type of number. In this article, we will understand the concept of perfect squares and also learn methods to identify them....Read MoreRead Less

Perfect squares are numbers that are the products of integers by themselves. In other words, when an integer is multiplied by itself, the resulting product is termed as a perfect square of the given number.

For example, 36 is a perfect square because it is the product of 6 by itself, 6\(\times\)6 = 36.

So, we can express a perfect square as p\(^2\), where p is an integer.

Natural number | Perfect square |
---|---|

1 | 1 \(\times\) 1 = 1 |

2 | 2 \(\times\) 2 = 4 |

3 | 3 \(\times\) 3 = 9 |

4 | 4 \(\times\) 4 = 16 |

5 | 5 \(\times\) 5 = 25 |

6 | 6 \(\times\) 6 = 36 |

7 | 7 \(\times\) 7 = 49 |

8 | 8 \(\times\) 8 = 64 |

9 | 9 \(\times\) 9 = 81 |

10 | 10 \(\times\) 10 = 100 |

11 | 11 \(\times\) 11 = 121 |

12 | 12 \(\times\) 12 = 144 |

13 | 13 \(\times\) 13 = 169 |

14 | 14 \(\times\) 14 = 196 |

15 | 15 \(\times\) 15 = 225 |

16 | 16 \(\times\) 16 = 256 |

17 | 17 \(\times\) 17 = 289 |

18 | 18 \(\times\) 18 = 324 |

19 | 19 \(\times\) 19 = 361 |

20 | 20 \(\times\) 20 = 400 |

21 | 21 \(\times\) 21 = 441 |

22 | 22 \(\times\) 22 = 484 |

23 | 23 \(\times\) 23 = 529 |

24 | 24 \(\times\) 24 = 576 |

25 | 25 \(\times\) 25 = 625 |

**Example 1: The area of a circle is 45,216 square feet. What is the radius of the circle?**

**Solution:**

Given, the area of the circle = 45,216 square feet

The area of a circle \(A=r^2\)

\(45,216=3.14~r^2\)

\(r^2=\frac{45,216}{3.14}=14400\)

\(r=\sqrt{14400}\)

\(r=120\) feet

Hence, the radius of the circle is 120 feet.

**Example 2: Find the perfect square of 15.**

**Solution:**

Given number = 15

To find the perfect square, multiply the number by itself

Therefore, 15 \(\times\) 15 = 225

Hence, the perfect square of 15 is 225.

**Example 3: Evaluate the expression \(5\sqrt{9}+10\)****.**

**Solution:**

Given expression, \(5\sqrt{9}+10\)

Since the square of 3 is 9, that is, \(\sqrt{9}=3\)

So, \(5\sqrt{9}+10\)

= \(5\times3+10\)

= 15 + 10

= 25

Hence, \(5\sqrt{9}+10=25\).

Frequently Asked Questions on Perfect Squares

There are four perfect squares between 1 and 20: \(1^2,2^2,3^2,\) and \(4^2\).

They are: 1, 4, 9, 16.

Yes, 196 is a perfect square of 14, \(14^2=196\)

A number is a perfect square if the square root of the number is an integer. The square root of 120 is approximately 10.954. The square root of 120 is not an integer. Hence, 120 is not a perfect square.

The perfect square of 25 is 625, that is, \(25^2=625\).

A number is considered to be a perfect square if it can be written as a square of an integer, that is, if it is a product of a number when multiplied by the number itself.