What is a square root calculator?
A square root calculator is an online tool that finds the square root of a number. It can quickly calculate exact or decimal square root results without requiring manual mathematical calculations.
Square Root Calculator
Find square roots instantly, or switch to any nth root when you need cube roots, fourth roots, and more.
Enter a number and root index
Use root index 2 for a square root, 3 for a cube root, or any positive whole number for an nth root.
About this calculator
How to use Square Root Calculator, plus the formulas and logic behind the results.
Tool description
The Square Root Calculator finds square roots and other nth roots. It also verifies the result by raising it back to the chosen root index.
How to use
- Enter the number under the radical.
- Set the root index (2 for square root, 3 for cube root, and so on).
- Select Calculate to see the root and a verification value.
- Even roots of negative numbers are rejected because they are not real.
Formulas & reference
ⁿ√x = x^(1/n) for x ≥ 0Odd roots of negative x: −(|x|^(1/n))Verification: result^n ≈ original input
Common roots at a glance
- Square root: n = 2, e.g. √144 = 12
- Cube root: n = 3, e.g. ∛27 = 3
- Fourth root: n = 4
- Even roots of negative numbers are not real
Calculation logic
The calculator uses real-number power arithmetic. Even roots require a non-negative input. Odd roots of negatives are computed from the absolute value and then signed.
Results are shown in decimal form. Very large roots may produce rounding differences in the verification step.
Square Root Calculator FAQ
Common questions about this calculator and how to use the results.
How do you calculate a square root?
The square root of a number is a value that, when multiplied by itself, produces the original number. For example, the square root of 25 is 5 because 5 × 5 = 25.
What is the square root of a number?
The square root of a number is a value that produces that number when multiplied by itself. For example, √16 = 4 because 4² = 16.
How does a square root calculator work?
A square root calculator uses a mathematical algorithm to determine the value that, when squared, equals the input number. It can provide exact values for perfect squares and decimal approximations for other numbers.
How do you find the square root without a calculator?
For perfect squares, you can memorize common square roots such as √25 = 5 and √100 = 10. For non-perfect squares, methods such as estimation, long division, or the Newton-Raphson method can be used.
What is the square root of 2?
The square root of 2 is an irrational number, approximately equal to 1.41421356. Its decimal representation continues indefinitely without repeating.
What is the square root of 4?
The principal square root of 4 is 2 because 2 × 2 = 4. In equation solving, both 2 and -2 have a square of 4, but √4 specifically refers to the principal, non-negative square root.
What is the square root of 9?
The principal square root of 9 is 3 because 3 × 3 = 9. In the equation x² = 9, however, both x = 3 and x = -3 are solutions.
Can a square root calculator calculate negative numbers?
A standard real-number square root calculator cannot return a real result for a negative number. The square root of a negative number involves imaginary numbers, such as √-1 = i.
Can you calculate the square root of a decimal?
Yes. A square root calculator can calculate the square root of decimal values. For example, the square root of 0.25 is 0.5 because 0.5 × 0.5 = 0.25.
How do you simplify a square root?
To simplify a square root, factor the number and remove any perfect-square factors from under the radical. For example, √12 can be simplified to 2√3.
What is the difference between a square and a square root?
Squaring a number means multiplying it by itself, such as 5² = 25. A square root works in the opposite direction: √25 = 5.