Root calculators

These root calculators provide three tools to compute roots of numbers. It includes a square root calculator, a cube root calculator, and a general root calculator where you can specify both the number and the root (e.g., 4th root or 5th root).

Related calculators:

What is a root?

A root of a number is a value that, when raised to a specific power, equals the original number.

In general:

• For a number x and a root n, the n-th root of x is a value r such that:

r^n = x

For example:

• The square root of 16 (\sqrt{16}) is 4 because 4^2=16
• The cube root of 27 (\sqrt[3]{27}) is 3 because 3^3=27

How can a root be found in general?

To find the n-th root of a number x, you use the formula:

r = x^{\frac{1}{n}}

• Here, \frac{1}{n}​ is the reciprocal of n.
• This formula works for any positive number xxx and positive integer n.

In programming, most modern languages, including JavaScript, use the Math.pow(x, 1/n) or x ** (1/n) methods for general root calculation.

How can a square root be found?

The square root of a number x is a value r such that:

r^2 = x

• Formulaically, it is:

r = x^{\frac{1}{2}} \quad \text{or} \quad \sqrt{x}

Example: \sqrt{9}=3 because 3^2=9

In practice, you can:

1. Use the formula r=x^{0.5}.
2. Use a calculator or programming library function like Math.sqrt(x) in JavaScript.

How can a cube root be found?

The cube root of a number x is a value r such that:

r^3 = x

• Formulaically, it is:

r = x^{\frac{1}{3}} \quad \text{or} \quad \sqrt[3]{x}

Example: \sqrt[3]{8}=2 because 2^3=8

In practice, you can:

1. Use the formula r=x^{\frac{1}{3}}.
2. Use a calculator or programming library function like Math.cbrt(x) in JavaScript.

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