# 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\(\sqrt[10]{d^{7}}\).

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