How to Find Value of Root on Calculator

Finding the value of a root on a calculator is a fundamental mathematical operation that appears in many scientific and everyday calculations. This guide explains how to perform root calculations using both calculator methods and manual techniques.

How to Use the Calculator

The calculator on this page provides a quick way to find root values. Simply enter the number you want to find the root of and select the type of root (square root, cube root, etc.). The calculator will display the result immediately.

Tip: For more precise calculations, use the scientific notation option when entering very large or very small numbers.

Step-by-Step Instructions

Enter the number you want to find the root of in the "Number" field.
Select the type of root you want to calculate from the dropdown menu.
Click the "Calculate" button to see the result.
Review the result and use the "Reset" button to clear the calculator for a new calculation.

Example Calculation

Let's find the square root of 144 using the calculator:

Enter "144" in the number field.
Select "Square Root" from the dropdown.
Click "Calculate".
The result will display "12" as the square root of 144.

Manual Method

If you don't have access to a calculator, you can find root values manually using estimation techniques. This method is less precise but useful for quick approximations.

Square Root Estimation

To estimate the square root of a number:

Find two perfect squares between which your number lies.
Divide your number by one of these perfect squares to get an approximate root.
Refine your estimate by averaging with the perfect square.

Example: To find √45:

49 (7²) is greater than 45, and 36 (6²) is less than 45.
Divide 45 by 6 to get 7.5.
Average 7.5 with 6 to get 6.75 as a better estimate.

Cube Root Estimation

For cube roots, use similar techniques but with perfect cubes:

Find two perfect cubes around your number.
Divide your number by the cube root of the lower perfect cube.
Refine by averaging with the cube root of the higher perfect cube.

Common Roots

Here are some frequently used roots and their properties:

Root Type	Symbol	Definition	Example
Square Root	√x	Number that, when multiplied by itself, gives x	√16 = 4
Cube Root	∛x	Number that, when multiplied by itself three times, gives x	∛27 = 3
Fourth Root	⁴√x	Number that, when multiplied by itself four times, gives x	⁴√16 = 2

Note: For even roots (like square roots), the result is always non-negative. For odd roots (like cube roots), the result maintains the sign of the original number.

FAQ

What is the difference between a square root and a cube root?: A square root is a number that, when multiplied by itself, gives the original number. A cube root is a number that, when multiplied by itself three times, gives the original number.
Can I find roots of negative numbers?: Yes, you can find roots of negative numbers for odd roots (like cube roots). For even roots (like square roots), the result is not a real number but an imaginary number.
How accurate are calculator root calculations?: Most scientific calculators provide accurate results to at least 10 decimal places. For more precise calculations, you may need specialized software.
What is the difference between √ and ∛ symbols?: The √ symbol represents a square root, while the ∛ symbol represents a cube root. The number of lines under the radical symbol indicates the root's degree.

About this calculator

Written by Calculator Editorial TeamPractical calculator research and UX writing

Reviewed by Practical Tools ReviewFormula logic, assumptions, and usability checks

Updated June 25, 2026. Formulas, assumptions, and limitations are shown directly on this page.

Formula and Source

The calculator uses standard mathematical formulas for root calculations. For square roots, it uses the √x formula, and for cube roots, it uses the ∛x formula.

Sources: National Institute of Standards and Technology (NIST), International Organization for Standardization (ISO)