Nth Root of A Number Calculator to 15 Places

The nth root of a number is a value that, when raised to the power of n, gives the original number. This calculator computes the nth root with precision to 15 decimal places, which is useful for mathematical, scientific, and engineering applications.

What is the nth root?

The nth root of a number x is a number y such that y raised to the power of n equals x. Mathematically, this is expressed as:

y = x^(1/n)

For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. The square root is a special case where n=2.

Roots are fundamental in mathematics and appear in various fields including algebra, calculus, and physics. Calculating roots with high precision is essential for advanced computations.

How to calculate the nth root

To calculate the nth root of a number, you can use the following steps:

Identify the number (x) and the root index (n).
Use the formula: y = x^(1/n).
For non-integer roots, use logarithms or iterative methods for high precision.
Round the result to the desired number of decimal places.

Our calculator implements this formula with JavaScript's Math.pow() function for integer roots and a custom iterative method for non-integer roots to ensure 15 decimal place precision.

Note: For non-integer roots, the result may be an irrational number that cannot be expressed as a finite decimal.

Examples of nth roots

Here are some examples of nth roots calculated to 15 decimal places:

Number (x)	Root Index (n)	nth Root (y)
27	3	3.000000000000000
16	2	4.000000000000000
2	4	1.189207115002721
1000	3	10.000000000000000
1.44	2	1.200000000000000

These examples demonstrate how the nth root calculator provides precise results for various combinations of numbers and root indices.

FAQ

What is the difference between a square root and a cube root?: The square root (n=2) finds a number that, when multiplied by itself, gives the original number. The cube root (n=3) finds a number that, when multiplied by itself three times, gives the original number.
Can I calculate roots of negative numbers?: Yes, but the results will be complex numbers for odd roots and real numbers for even roots. Our calculator handles both cases.
How precise are the results?: The calculator provides results to 15 decimal places, which is sufficient for most mathematical and scientific applications.
What if I enter a non-integer root index?: The calculator uses an iterative method to compute non-integer roots with high precision. The result may be an irrational number.