This calculator helps you find the nth root of any number. Use it to calculate square roots, cube roots, or any custom root.
The Root Calculator is an advanced mathematical tool designed to help you calculate square roots, cube roots, and nth roots of any positive or negative number. Whether you're a student solving algebra homework or a professional dealing with engineering calculations, this tool provides instant results with step-by-step solutions.
A root of a number is a value that, when multiplied by itself a certain number of times, gives the original number. The most common roots are:
The square root of a number x is a value y such that y² = x. For example:
Some numbers, like 2 or 7, don't have a whole-number square root. They are called irrational numbers and are usually represented with a decimal approximation (e.g., √2 ≈ 1.414).
The cube root of a number x is a value y such that y³ = x. For example:
Cube roots work for both positive and negative numbers. For example, ∛(-8) = -2.
The nth root generalizes square and cube roots. It refers to a value that, when raised to the power of n, gives the original number:
ⁿ√x = x^(1/n)
Example: ⁵√243 = 3 (because 3^5 = 243)
Find: ⁴√81
Roots of decimal or non-perfect powers are calculated using exponent rules:
⁵√10 ≈ 10^(1/5) ≈ 1.5849
The calculator supports up to 10 decimal places for precision.
Cube roots and odd-index roots of negative numbers are defined:
However, even-index roots of negative numbers are undefined in real numbers (e.g., √(-4) is imaginary).
The calculator supports root calculations with scientific notation:
√(1.6 × 10⁴) = √16000 ≈ 126.49
| Number | Square Root | Cube Root | ⁴th Root |
|---|---|---|---|
| 4 | 2 | 1.5874 | 1.4142 |
| 16 | 4 | 2.5198 | 2 |
| 81 | 9 | 4.3267 | 3 |
| 243 | 15.588 | 6.2403 | 4.5 |
Free online Root Calculator to compute square roots, cube roots, and nth roots of any number. Supports step-by-step solutions, negative inputs, and high precision.
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The Root Calculator simplifies complex root calculations for square, cube, and nth roots. With support for decimals, negative numbers, and scientific notation, it’s a versatile tool for students, teachers, and professionals alike. Whether you're learning algebra or working with advanced formulas, this calculator gives you the accuracy and clarity you need.
Roots and exponents are inverse operations. If an exponent raises a number to a power, a root brings it back down:
This relationship is essential in algebra, calculus, and higher-level mathematics. The root calculator uses this inverse logic to compute results for fractional and decimal exponents as well.
When dealing with roots of numbers raised to negative exponents, the rules still apply:
Example: 4^(-1/2) = 1 / √4 = 1/2
Our calculator supports negative and fractional exponents, making it ideal for calculus students and engineers.
Roots are fundamental in calculating diagonals of squares and rectangles using the Pythagorean Theorem:
Diagonal (d) = √(a² + b²)
Whether you’re designing a ramp, staircase, or a sloped roof, root calculations ensure precise angle and material measurements.
The Root Calculator is ideal for data analysts performing statistical calculations manually or for educational purposes.
Exams like SAT, GRE, GMAT, JEE, NEET, and SSC often test your ability to solve root-based problems. Mastering square roots, cube roots, and simplification techniques is essential for:
Use our tool to improve your speed and accuracy for competitive preparation.
While our basic Root Calculator focuses on real numbers, it can detect when a result is undefined in the real domain. For example:
Advanced versions of this calculator (coming soon) will include complex root computations.
Problem: A square garden has an area of 324 square meters. What is the length of one side?
Solution: side = √324 = 18 meters
Problem: A cube has a volume of 1000 cubic cm. What is the length of one edge?
Solution: edge = ∛1000 = 10 cm
The calculator accepts standard keyboard formats for ease of use across devices.
The concept of square roots dates back to the Babylonians (2000 BCE), who used geometric methods to approximate roots. In ancient India, Aryabhata and Bhaskara introduced early algebraic rules for root extractions, including square and cube roots. Modern calculators and computers now use logarithmic and iterative algorithms for root calculations with high precision.
We are working on advanced features such as:
Stay tuned for updates to make root calculations even more powerful!
Whether you're simplifying radicals, solving algebraic equations, or finding roots in real-life problems, our Root Calculator is your go-to solution. Simple, accurate, and lightning-fast — start calculating now!