Square Root
Definition
A value that, when multiplied by itself, gives the original number. The square root of 25 is 5 because 5 × 5 = 25.
Why is Square Root Important?
Square Root is a foundational mathematical concept used across science, engineering, finance, and everyday problem-solving. From analyzing data sets to optimizing business decisions, this concept provides the analytical framework needed to interpret quantitative information accurately.
Our math calculators make complex computations simple and accessible, providing step-by-step results that help students, professionals, and curious minds explore mathematical relationships with confidence.
What is a Square Root?
The square root of a number x is a value y such that y² = x. Written as √x or x^(1/2). For example, √25 = 5 because 5² = 25. Every positive number has two square roots (positive and negative), but √ conventionally refers to the positive (principal) root.
Perfect Squares Reference
| √n | n | √n | n |
|---|---|---|---|
| √1 = 1 | 1 | √121 = 11 | 121 |
| √4 = 2 | 4 | √144 = 12 | 144 |
| √9 = 3 | 9 | √169 = 13 | 169 |
| √16 = 4 | 16 | √196 = 14 | 196 |
| √25 = 5 | 25 | √225 = 15 | 225 |
| √36 = 6 | 36 | √256 = 16 | 256 |
| √49 = 7 | 49 | √289 = 17 | 289 |
| √64 = 8 | 64 | √324 = 18 | 324 |
| √81 = 9 | 81 | √400 = 20 | 400 |
| √100 = 10 | 100 | √625 = 25 | 625 |
Square Root Properties
- √(a × b) = √a × √b → √50 = √25 × √2 = 5√2
- √(a / b) = √a / √b → √(9/16) = 3/4
- √a² = |a| (always positive)
- Square root of a negative number is imaginary: √(-1) = i