Square Root Calculator

Square root calculator for perfect squares, decimals, and quick checks

A square root tells you which number, when multiplied by itself, gives the original value. If you are checking homework, scaling a recipe, working with areas, or sanity-checking a figure in a spreadsheet, the most common question is simple: “What is √x?” This square root calculator is built for that everyday intent. You enter a non-negative number (whole number or decimal) and get an immediate square root result, plus a few extra cues that help you interpret it.

The first output is the square root value itself, rounded to a sensible number of decimal places. In many real situations you do not need 15 digits of precision, but you also do not want a result that is so rounded it becomes misleading. That is why the default view gives a practical answer quickly, and the optional advanced setting lets you change how many decimal places you want to display.

The calculator also checks whether your input is a perfect square (for whole numbers). If it is, the square root is an exact whole number (for example, √144 = 12). If it is not, the calculator shows the nearest lower and upper perfect squares. This helps you judge whether your answer makes sense at a glance. For example, if your number sits between 121 and 144, you already know the square root must sit between 11 and 12.

Assumptions and how to use this calculator

• The input must be a real, non-negative number. Negative inputs do not have a real square root, so the calculator will stop and show an error.
• For decimal inputs, the square root is shown as a rounded approximation. Rounding is controlled by “Decimal places” (default is 6).
• Perfect-square checks and “nearest perfect squares” are meaningful for whole-number inputs. If you enter a decimal, the “perfect square” concept does not apply in the same way.
• Simplified radical form (like 2√3) is only attempted for whole numbers and is skipped for very large values to avoid slow processing in the browser.
• All results are computed using standard real-number arithmetic. Extremely large numbers may lose some integer precision due to normal JavaScript number limits.

Common questions

Why does the calculator reject negative numbers?

This calculator is for real-number square roots. In real numbers, no number squared becomes negative, so √(-9) is not a real value. If you specifically need complex-number square roots, that is a different tool and a different intent.

What does “nearest perfect squares” mean, and why should I care?

Perfect squares are numbers like 0, 1, 4, 9, 16, 25, 36, and so on. Their square roots are whole numbers. If your input is not a perfect square, finding the nearest perfect squares brackets the answer. It is a fast error-check: if your square root result falls outside that bracket, something is wrong.

How many decimal places should I use?

Use the smallest number that still supports your decision. For quick checks, 2 to 4 decimals is usually enough. For geometry or engineering approximations, 4 to 8 decimals is common. More decimals look “more accurate,” but if your original input is estimated, extra decimals are fake precision.

What is “simplified radical form,” and when does it matter?

For some whole numbers, you can rewrite the square root in a cleaner exact form by factoring out a square. Example: √12 can be simplified to 2√3 because 12 = 4×3 and √4 = 2. This is mainly useful in algebra and exact-form math problems, not in most everyday measurement tasks.

Why might the simplified radical form be skipped for large numbers?

Simplifying radicals requires factoring the number to find square factors. That can become slow for very large integers in a browser tab. When the number is above a practical threshold, the calculator prioritizes responsiveness and shows the numeric square root and perfect-square context instead.