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Square Root Calculator - Root and Power Calculator

Free square root calculator for square roots, cube roots, nth roots, and powers. Includes radical simplification and perfect square check.

Square Root Calculator

Calculate square roots, cube roots, and powers easily

Which mathematical operation do you want to perform?

Number to find root or power of

Which degree root do you want to find?

What power do you want to raise the number to?

How many decimal places to show in the result?

Result

Enter your values to see results

and click the "Calculate" button

What is a Square Root?

A square root is a value that, when multiplied by itself, gives the original number. For example, since 5 × 5 = 25, the square root of 25 is 5. Mathematically written as √25 = 5. The square root symbol (√) is called a 'radical.' Square root calculations are used in area calculations, engineering, physics, and many other fields. This tool supports square roots, cube roots, nth roots, and powers.

How to Use This Calculator

  1. Select the operation type (square root, cube root, etc.)
  2. Enter the number
  3. For nth root, specify the degree
  4. Click Calculate to see the result

Root Formulas

√x = x^(1/2), ∛x = x^(1/3), ⁿ√x = x^(1/n)

Roots and exponents are inverse operations. The square root of x equals x raised to the 1/2 power.

Frequently Asked Questions

What is a square root?
A square root is a value that, when multiplied by itself, gives the original number. √25 = 5 because 5 × 5 = 25. Mathematically, if x² = a then x = √a. The symbol (√) is called a 'radical.'
Can you take the square root of a negative number?
Not in real numbers - no real number squared gives a negative result. In complex numbers, √(-1) = i (imaginary unit). For example, √(-9) = 3i. Note: Odd roots of negative numbers are defined, e.g., ∛(-8) = -2.
How do you simplify a square root?
Factor the number and pull out perfect square factors. Example: √72 = √(36 × 2) = √36 × √2 = 6√2. This is called 'simplifying radicals' and is common in math problems.
What's the difference between square root and cube root?
Square root (√) is the second root: if x² = a then √a = x. Cube root (∛) is the third root: if x³ = a then ∛a = x. Key difference: Cube roots work for negative numbers (∛-8 = -2), square roots don't.
What is a perfect square?
A perfect square is a number that is the square of an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Perfect squares have integer square roots. Non-perfect squares (like 2, 3, 5) have irrational square roots.
How is the Pythagorean theorem related to square roots?
The hypotenuse of a right triangle is c = √(a² + b²). Example: legs of 3 and 4 give hypotenuse = √(9 + 16) = √25 = 5. This formula is used in distance calculations, engineering, and geometry.

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