About the Square Root Calculator
What is the Square Root Calculator?
The square root of a number x is the value that, multiplied by itself, gives x: √49 = 7 because 7 × 7 = 49. Every positive number has two square roots (+7 and −7); the √ symbol means the positive one, called the principal square root.
For whole numbers the calculator also writes the root in simplest radical form by taking the largest perfect-square factor outside the root sign — √72 = √(36 × 2) = 6√2 — which is the form expected in school algebra and geometry answers.
How to use the Square Root Calculator
- Number — any number ≥ 0; decimals are allowed (radical form is shown for whole numbers). (sample: 72)
- Press Find Square Root (results also refresh as you type). The result card shows the Square Root, along with Simplest radical form, Perfect square? and Check: root².
Formula used
√(a² × b) = a√b
- a² = the largest perfect square that divides the number
- b = the remaining factor left under the root
Negative numbers have no real square root (√−1 = i is imaginary); use the Complex Number Calculator for those.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Number | 72 |
| Result | Value |
|---|---|
| Square Root | 8.48528137 |
| Simplest radical form | 6√2 |
| Perfect square? | No |
| Check: root² | 72 |
Tips for using the Square Root Calculator
- Perfect squares worth remembering: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
- √(a × b) = √a × √b, but √(a + b) is not √a + √b.
- To estimate a root, find the perfect squares on either side: √72 lies between √64 = 8 and √81 = 9.