Question

What is 2 3/2 equal to?

Answer 1

Answer:

  (a)  √8

Step-by-step explanation:

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

Indices

The relationship of indices to radicals is ...

  $\large{\sqrt[n]{a^m}}={a^{\frac{m}{n}}$

Application

The given expression can be rewritten as ...

  $2^{\frac{3}{2}}=\sqrt[2]{2^3}=\boxed{\sqrt[2]{8}}$

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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.

  $\sqrt[2]{8}=\sqrt{8}=2\sqrt{2}$