Square Root Calculator
Frequently Asked Questions
What is the square root of a number?
The square root of a number is the value that, when multiplied by itself, gives the original number. For example, the square root of 49 is 7 because 7 × 7 = 49. Every positive number has a principal (positive) square root and a negative counterpart.
Can I calculate the square root of a decimal number?
Yes. The calculator accepts any positive decimal number. For instance, the square root of 2.25 is 1.5, and the square root of 0.01 is 0.1. Simply type the decimal into the input field and click Calculate to get the precise result instantly.
Why does the square root of 2 never end?
√2 is an irrational number, meaning its decimal expansion is infinite and non-repeating (1.41421356…). It cannot be expressed as a simple fraction. Most non-perfect-square integers produce irrational square roots. Perfect squares like 4, 9, and 16 are the exception, giving clean whole-number results.
What is the square root of a negative number?
Negative numbers do not have real square roots because no real number multiplied by itself gives a negative result. In advanced mathematics, the square root of −1 is defined as the imaginary unit i. Our calculator works with non-negative real numbers only, as negative input falls outside real-number arithmetic.
How do I simplify a square root like √72?
Factor out the largest perfect square: √72 = √(36 × 2) = √36 × √2 = 6√2. Always look for perfect square factors (4, 9, 16, 25, 36…) inside the radical. Simplifying gives an exact form that is more useful in algebra than the decimal approximation 8.4853.
Recommended
Related Tools
BMI Calculator
Calculate your BMI from height and weight and get a detailed health report with BMI category, healthy weight range, body fat estimate, calories, macros and more.
Average Calculator
Percentage Calculator
Calculate percentages, find increase/decrease, reverse percent, and tip — four modes, instant results.
Tip Calculator
Calculate the tip amount and split the bill between any number of people instantly.
Discount Calculator
Calculate the sale price after a percentage discount, or find what discount percentage was applied.