How to Use Calculator to Find 3rd Nth Root

What is an nth Root?

The nth root of a number is a value that, when raised to the power of n, gives the original number. For example, the cube root (3rd root) of 27 is 3 because 3 × 3 × 3 = 27.

Mathematically, the nth root of a number x is written as x^(1/n). For example, the 3rd root of 8 is 8^(1/3) = 2.

Using a Calculator to Find nth Roots

Most scientific calculators have a built-in function to find nth roots. Here's how to use it:

1. Enter the number you want to find the root of.
2. Press the "y√x" or "nth root" function (this may be labeled differently on different calculators).
3. Enter the value of n (the root you want to find).
4. Press the equals (=) button to get the result.

For example, to find the 3rd root of 64:

1. Enter 64.
2. Press the "y√x" function.
3. Enter 3.
4. Press = to get the result 4.

The Formula for nth Roots

The general formula for finding the nth root of a number x is:

This formula can be used to find any root of any number, whether it's the square root (n=2), cube root (n=3), or any other root.

For example:

• Square root of 16: 16^(1/2) = 4
• Cube root of 27: 27^(1/3) = 3
• 4th root of 16: 16^(1/4) = 2

Worked Examples

Example 1: Finding the 3rd Root of 27

Using the formula:

Because 3 × 3 × 3 = 27.

Example 2: Finding the 5th Root of 32

Using the formula:

Because 2 × 2 × 2 × 2 × 2 = 32.

Example 3: Finding the 4th Root of 81

Using the formula:

Because 3 × 3 × 3 × 3 = 81.

Common Mistakes

When finding nth roots, it's easy to make a few common mistakes:

1. Confusing roots with exponents: Remember that the nth root is the inverse of raising to the nth power. For example, 2^3 = 8, but the cube root of 8 is 2.
2. Using the wrong root: Always double-check which root you're trying to find (square root, cube root, etc.).
3. Negative numbers with even roots: Remember that even roots of negative numbers are not real numbers. For example, the square root of -4 is not a real number.