Square roots turn areas into lengths, appear in the Pythagorean theorem, standard deviations and the quadratic formula, and describe how many things scale: doubling the area of a square multiplies its side by √2.
How to use the Square Root Calculator
- Enter your number
- Number to square
- Every result field is editable: type into Square root √x and Enter your number plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
The principal (non-negative) square root is computed. The nearest perfect squares show between which whole numbers the root lies. Type a root into the result to find its square.
Inputs explained
| Field | What to enter |
|---|---|
| Enter your number | A number |
| Number to square | A number |
What each result means
- Square root √x = sqrt([Enter your number])
- Largest perfect square ≤ x = floor(sqrt([Enter your number]))^2
- Smallest perfect square ≥ x = ceil(sqrt([Enter your number]))^2
- Square of the second number = [Number to square]^2
Example values
How the main result changes when Enter your number changes and everything else stays at the example values above:
| Enter your number | Square root √x |
|---|---|
| 25 | 5 |
| 37.5 | 6.1237 |
| 50 | 7.0711 |
| 62.5 | 7.9057 |
| 75 | 8.6603 |
| 100 | 10 |
Formula
√x = y ⇔ y² = x (y ≥ 0)
Worked example
Inputs: Enter your number: 50; Number to square: 12.
Results: Square root √x = 7.0710678119; Largest perfect square ≤ x = 49; Smallest perfect square ≥ x = 64; Square of the second number = 144.
Key terms
- Principal square root
- The non-negative square root √x.
Frequently asked questions
What is the square root of 50?
About 7.0711; exactly 5√2.
Does a number have two square roots?
Yes, ±√x, but √x means the non-negative one.
What is the square root of a negative number?
Not real, though √−1 = i in the complex numbers.
How can I estimate √50?
It is between √49 = 7 and √64 = 8, close to 7.