Simplify 8 square root of 27

$8 \sqrt{27}$

Step 1

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$8 \sqrt{9 (3)}$

Rewrite $9$ as $3^{2}$ .

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

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

Step 2

Pull terms out from under the radical.

$8 (3 \sqrt{3})$

Step 3

Multiply $3$ by $8$ .

$24 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$24 \sqrt{3}$

Decimal Form:

$41.56921938 \dots$

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