Which of the following is the radical expression of 2d^7/10?
\(\sqrt[7]{2}d^{10}\), \(\sqrt[10]{2}d^{7}\),  2\(\sqrt[10]{d^{7}}\), 2\(\sqrt[7]{d^{10}}\)

Solution:

If n is a positive integer that is greater than x and a is a real number or a factor, then

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

Here, 7/10 is a non-integer rational exponent.

Using (1) above \(2d^{\frac{7}{10}}\) can be converted into a radical in the following manner:

In the given problem, a = d; n = 10 and x = 2 Therefore ,

\(2d^{\frac{7}{10}}\) = 2\(\sqrt[10]{d^{7}}\)

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 \(\sqrt[3]{x}\).

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

Which of the following is the radical expression of 2d^7/10?

Summary:

The radical expression of 2d^7/10 is 2\(\sqrt[10]{d^{7}}\).