Simplify 3 square root of square root of 64

$3 \sqrt{\sqrt{64}}$

Step 1

Rewrite $64$ as $8^{2}$ .

$3 \sqrt{\sqrt{8^{2}}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$3 \sqrt{8}$

Step 3

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

Factor $4$ out of $8$ .

$3 \sqrt{4 (2)}$

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

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

Step 4

Pull terms out from under the radical.

$3 (2 \sqrt{2})$

Step 5

Multiply $2$ by $3$ .

$6 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2}$

Decimal Form:

$8.48528137 \dots$