Evaluate 3^( square root of 8)

$3^{\sqrt{8}}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$3^{\sqrt{4 (2)}}$

Rewrite $4$ as $2^{2}$ .

$3^{\sqrt{2^{2} \cdot 2}}$

$3^{\sqrt{2^{2} \cdot 2}}$

Step 2

Pull terms out from under the radical.

$3^{2 \sqrt{2}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3^{2 \sqrt{2}}$

Decimal Form:

$22.36159093 \dots$

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