Question

What is 2 3/2 equal to?

Answer 1

(a) √8

Explanation:

You want to know the radical equivalent to 2^(3/2).

Indices

The relationship of indices to radicals is ...

`\large{\sqrt[n]{a^m}}={a^{(m)/(n)}`

Application

The given expression can be rewritten as ...

`2^{(3)/(2)}=\sqrt[2]{2^3}=\boxed{\sqrt[2]{8}}`

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Additional comment

When the index of the radical is 2, it is usually left off. The radical can be simplified by removing the perfect square factor.

`\sqrt[2]{8}=√(8)=2√(2)`