Square Root Calculator
Calculate the principal square root, simplified radical form, and nearest perfect squares of any number.
Number Input
Precision & Settings
The square root of a negative number results in an imaginary number (denoted by i), where i = √-1.
Calculation Results
Square Root Calculator — Simplify Radicals and Decimals
Have you ever stopped to think about what that radical symbol really means? It’s simply asking for the number that, when multiplied by itself, gives you the value inside. While perfect squares like 16 or 25 yield nice whole numbers, most numbers are irrational, leading to those never-ending decimals.
When it comes to math homework, just having a raw decimal often doesn’t cut it. You typically need to simplify the radical completely, turning something like √20 into 2√5. Just type in your number, and you’ll get both the exact decimal and the fully simplified radical form.
But this isn’t just for your algebra class! Carpenters and DIY enthusiasts frequently use square roots to determine diagonal lengths with the Pythagorean theorem (a² + b² = c²).
A quick note: While positive numbers technically have two roots (like 5 and -5), here you’ll always see the positive “principal” root. And if you try to calculate a negative number? Well, that takes you right into the realm of imaginary numbers (i).