Nth Root Calculator

Understanding Nth Roots

In mathematics, an nth root of a number 'x' is a number 'y' which when raised to the power of 'n' equals 'x'. In equation form, it is represented as $$y^n = x$$. The nth root can be written using a radical symbol as $$\sqrt[n]{x}$$, where 'n' is the index and 'x' is the radicand. For example, the square root (n=2) of 9 is 3 because $$3^2 = 9$$, and the cube root (n=3) of 8 is 2 because $$2^3 = 8$$. This calculator helps you find the approximate decimal value for any nth root, which is particularly useful when the root is not a whole number. It utilizes numerical methods to provide accurate approximations.

• Square Root (n=2): $$\sqrt{x}$$ (e.g., $$\sqrt{25} = 5$$)
• Cube Root (n=3): $$\sqrt[3]{x}$$ (e.g., $$\sqrt[3]{8} = 2$$)
• Fourth Root (n=4): $$\sqrt[4]{x}$$ (e.g., $$\sqrt[4]{16} = 2$$)
• ... and so on for any positive integer 'n'.