Which is the radical expression of 4d^3/8?

Solution:

If n is a positive integer that is greater than x and a is a real number or a factor, then we have a non-integer rational exponent.

\(a^{\frac{x}{n}} = \sqrt[n]{a^{x}}\)(1)

Using (1) above \(4d^{\frac{3}{8}}\) can be converted into a radical in the following manner:

In the given problem, a = d; n = 8 and x = 3 Therefore ,

\(4d^{\frac{3}{8}}\) = \(4\sqrt[8]{d^{3}}\)

In mathematics, a radical expression is defined as an expression containing a radical (√) symbol. Many people mistakenly call the symbol '√'a square root but actually, it is used to find a higher cube root also but then the representation is \(\sqrt[3]{n}\).

Higher roots can also be represented and n^th root is represented as \(\sqrt[3]{x}\).