Square Root Calculator
Get the decimal square root and the simplified radical form of a number.
How to use the Square Root Calculator
- Enter the number.
- Press Calculate. The result updates automatically as you type.
About the Square Root Calculator
The square root of a number is the value that, multiplied by itself, gives the original number. Perfect squares such as 49 or 144 have whole-number roots; most other numbers have irrational roots whose decimals never end or repeat, so math classes often ask for the exact simplified radical instead of a rounded decimal.
Square roots appear whenever you work backward from an area or apply the Pythagorean theorem: a square room of 200 ft² is about 14.14 ft on a side. The radical symbol means the principal (non-negative) root, but when solving equations such as x² = 50, remember both +√50 and −√50 are solutions.
Formula
√x = y ⇔ y² = x, with y ≥ 0
To simplify a radical, pull out the largest perfect-square factor: √50 = √(25 × 2) = √25 × √2 = 5√2. For negative numbers, √−x = i√x.
Example calculation
Using the default values:
- Number = 50
the calculator returns:
- Square root: 7.0710678119
- Simplified radical: 5√2
- Perfect square?: No
- Nearest perfect squares: 49 (7²) and 64 (8²)
Frequently asked questions
How do I simplify a square root?
Factor the number, find the largest perfect-square factor and take its root outside the radical. √72 = √(36 × 2) = 6√2.
What is the square root of a negative number?
It is not a real number. In complex numbers, √−9 = 3i, where i is the imaginary unit.
Is the square root of 2 rational?
No. √2 ≈ 1.41421356 is irrational, which means it cannot be written as a fraction of two whole numbers.
Last updated: · Category: Math calculators