Square Root Calculator
Find the square root of any number to high precision, with simplified radical form.
Enter your values to see the result.
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Read the privacy policyHow this calculation works
Understand the method, inputs and limits behind your result.
- Formula
- The principal square root y satisfies y² = x, with y ≥ 0.
- Variables
- Number
- Decimal places
- Units
- Use the units shown beside each input. Counts and ratios are dimensionless unless labeled otherwise.
- Example
- √72 ≈ 8.4852813742. 72 is not a perfect square, but it simplifies to 6√2 because 72 = 36 × 2 and √36 = 6.
- Assumptions
- The result follows the selected options and supplied inputs. Displayed values may be rounded; check input precision before using the result.
- Source
- ToolzHive calculation guide and calculator implementation. External reference verification is pending.
- Last reviewed
- Review date not yet recorded.
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Clear instructions
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How to use the Square Root Calculator
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.
- 1 Enter a number, whole or decimal.
- 2 Choose how many decimal places you need.
- 3 Read the square root, the perfect-square check and the simplified radical form.
Example and practical tips
√72 ≈ 8.4852813742. 72 is not a perfect square, but it simplifies to 6√2 because 72 = 36 × 2 and √36 = 6.
Frequently asked questions
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.
Practical guides
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How to Use Square Root Calculator
Calculate the square root of any number to up to 50 decimal places, check if it is a perfect square and see the simplified radical form. Free calculator.
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