# Square Root Calculator

The square root function is a function that takes a non-negative real number as its input and returns its square root as its output. The square root of a number is the number that, when multiplied by itself, equals the original number.$\sqrt{4}=\;2$2 Copy Result

Created by Wes Nolte.Last updated Apr 25, 2024.

## The Square Root Calculator Formula

$y = \sqrt{x}$

## Definition of the Square Root Function

The square root function is a function that takes a non-negative real number as its input and returns its square root as its output. The square root of a number is the number that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3, because 3 x 3 = 9. The square root function is often denoted by the symbol √. So, the square root of 9 can be written as √9 = 3. The square root function has a domain of all non-negative real numbers and a range of all non-negative real numbers. This means that the square root function can only be used with non-negative real numbers as its input, and it will always return a non-negative real number as its output.The graph of the square root function is a parabola that opens upward. The parabola has its vertex at the origin (0, 0). Here is a table of some examples of square roots:Number | Square root |
---|---|

9 | 3 |

16 | 4 |

25 | 5 |

36 | 6 |

49 | 7 |

## History of The Square Root

The history of the square root is long and complex, dating back to ancient times. The concept of square roots was first developed by the Babylonians, who used it to solve problems in geometry and astronomy. The ancient Greeks also studied square roots, and they developed a number of methods for finding them.In the Middle Ages, the study of square roots continued in Europe. The Italian mathematician Leonardo Fibonacci introduced the use of decimal notation for square roots, and he also developed a number of new methods for finding them. In the 17th century, the French mathematician René Descartes developed a new method for finding square roots, which is still used today.The square root has been used in a wide variety of applications throughout history. It has been used in architecture, engineering, navigation, and many other fields. The square root is also a fundamental concept in mathematics, and it is used in a wide variety of mathematical problems.Here is a brief timeline of the history of the square root:**2000 BC:**The Babylonians use square roots to solve problems in geometry and astronomy.**600 BC:**The ancient Greeks study square roots and develop a number of methods for finding them.**13th century:**The Italian mathematician Leonardo Fibonacci introduces the use of decimal notation for square roots.**17th century:**The French mathematician René Descartes develops a new method for finding square roots.**18th century:**The Scottish mathematician John Napier invents logarithms, which make it easier to find square roots.**19th century:**The development of computers makes it possible to find square roots very quickly.

## Relationship with Exponentials

The relationship between square roots and exponentials is that they are inverses of each other. This means that if you square a number, then take the square root of the result, you will get back the original number. For example, if you square 3, you get 9. If you then take the square root of 9, you get back 3.Exponentials and square roots can also be used to solve for unknown variables. For example, if you know that the square root of a number is 5, then you can square both sides of the equation to get the number itself. In this case, you would square both sides of the equation √x = 5 to get x = 25.Exponentials and square roots are both important concepts in mathematics, and they have many applications in science, engineering, and other fields. For example, exponentials are used to model the growth of populations and the decay of radioactive materials. Square roots are used to find the area of squares and the volume of cubes.Here are some examples of how square roots and exponentials are used in real life:**Square roots are used to find the area of a square.**The area of a square is equal to the square of its side length. For example, if the side length of a square is 5 meters, then the area of the square is 5 x 5 = 25 square meters.**Square roots are used to find the volume of a cube.**The volume of a cube is equal to the cube of its side length. For example, if the side length of a cube is 3 meters, then the volume of the cube is 3 x 3 x 3 = 27 cubic meters.**Exponentials are used to model the growth of populations.**The population of a species can be modeled by an exponential function. This means that the population will grow at a rate that is proportional to its size. For example, if the population of a species is 100 today, and it is growing at a rate of 10% per year, then the population will be 110 next year, 121 the year after that, and so on.**Exponentials are used to model the decay of radioactive materials.**The amount of radioactive material in a sample will decay at a rate that is proportional to its size. For example, if a sample of radioactive material has an initial mass of 100 grams, and it has a half-life of 10 years, then after 10 years, the sample will have a mass of 50 grams. After another 10 years, the sample will have a mass of 25 grams, and so on.