By ToolzHive
About this tool
The square root calculator finds √x to high precision, up to 50 decimal places, using exact integer arithmetic. It tells you whether the number is a perfect square, shows the simplified radical form for whole numbers (so √72 becomes 6√2) and handles negative numbers by showing the imaginary result.
How to use Square Root Calculator
- Enter a number, whole or decimal.
- Choose how many decimal places you need.
- Read the square root, the perfect-square check and the simplified radical form.
Worked example
√72 ≈ 8.4852813742. 72 is not a perfect square, but it simplifies to 6√2 because 72 = 36 × 2 and √36 = 6.
What is a square root?
The square root of x is the number that, multiplied by itself, gives x. √49 = 7 because 7 × 7 = 49.
How do I simplify a square root?
Find the largest perfect square that divides the number, take its root outside and leave the rest inside: √72 = √(36 × 2) = 6√2.
What is the square root of a negative number?
There is no real answer. In complex numbers, √−9 = 3i, where i is the square root of −1.
Put this guide into practice
- Square Root Calculator — Find the square root of any number to high precision, with simplified radical form.