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How to Take Root Other Than 2 on Calculator

Reviewed by Calculator Editorial Team

Calculating roots other than square roots (2nd roots) is a fundamental mathematical operation that extends beyond the familiar square root. This guide explains how to calculate different types of roots using a calculator, including cube roots, fourth roots, and nth roots, with practical examples and step-by-step instructions.

What Are Roots?

In mathematics, a root of a number is a value that, when raised to a power, gives the original number. The most common root is the square root, which is the 2nd root. However, roots can be of any order, such as cube roots (3rd roots), fourth roots (4th roots), and so on.

For a number a and a positive integer n, the nth root of a is a number x such that:

xn = a

For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Different Types of Roots

Roots can be categorized based on their order:

  • Square Root (2nd Root): The most common root, denoted as √a. For example, √9 = 3.
  • Cube Root (3rd Root): Denoted as ∛a. For example, ∛27 = 3.
  • Fourth Root (4th Root): Denoted as ∜a. For example, ∜16 = 2.
  • Nth Root: General term for any root, denoted as n√a. For example, 5√32 = 2.

Each type of root has specific properties and applications in mathematics and real-world problems.

How to Calculate Roots

Calculating roots involves finding the number that, when raised to a specific power, equals the original number. Here's a general method for calculating nth roots:

  1. Identify the number (a) and the root order (n).
  2. Find the nth root of a by solving the equation xn = a.
  3. For non-integer roots, use a calculator or mathematical software.

Note: For non-integer roots, the result may not be exact and may require approximation.

Using a Calculator

Most scientific calculators have a dedicated root function or can calculate roots using exponentiation. Here's how to use a calculator to find roots:

  1. Enter the number you want to find the root of.
  2. Press the root function button (often labeled as "√" for square root or "y√x" for nth root).
  3. If calculating an nth root, enter the root order (n) and the number (a).
  4. Press the equals button to get the result.

For example, to calculate the cube root of 27:

  1. Enter 27.
  2. Press the cube root button (∛).
  3. The result will be 3.

Common Root Calculations

Here are some common root calculations and their results:

Root Type Example Result
Square Root (2nd Root) √16 4
Cube Root (3rd Root) ∛64 4
Fourth Root (4th Root) ∜16 2
Fifth Root (5th Root) 5√32 2

These examples demonstrate how different types of roots can be calculated and their corresponding results.

FAQ

What is the difference between a square root and a cube root?
The square root (2nd root) is the number that, when multiplied by itself, gives the original number. The cube root (3rd root) is the number that, when multiplied by itself three times, gives the original number.
How do I calculate a fourth root?
To calculate a fourth root, use the formula x = a^(1/4). For example, the fourth root of 16 is 2 because 2 × 2 × 2 × 2 = 16.
Can I calculate roots of negative numbers?
Yes, you can calculate roots of negative numbers for odd roots (e.g., cube roots). For even roots (e.g., square roots), negative numbers do not have real roots.
What is the nth root formula?
The nth root of a number a is given by the formula x = a^(1/n). For example, the fifth root of 32 is 2 because 2 × 2 × 2 × 2 × 2 = 32.
How do I use a calculator to find roots?
Most scientific calculators have a root function. Enter the number, press the root button, and then enter the root order if needed. Press equals to get the result.