Evaluate 9^( square root of 8)

$9^{\sqrt{8}}$

Step 1

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

Factor $4$ out of $8$ .

$9^{\sqrt{4 (2)}}$

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

$9^{\sqrt{2^{2} \cdot 2}}$

$9^{\sqrt{2^{2} \cdot 2}}$

Step 2

Pull terms out from under the radical.

$9^{2 \sqrt{2}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9^{2 \sqrt{2}}$

Decimal Form:

$500.04074929 \dots$

Related Questions