Simplify square root of 72 square root of 32 square root of 8

$\sqrt{72} \sqrt{32} \sqrt{8}$

Step 1

Combine using the product rule for radicals.

$\sqrt{72 \cdot 32} \sqrt{8}$

Step 2

Combine using the product rule for radicals.

$\sqrt{72 \cdot 32 \cdot 8}$

Step 3

Multiply.

Multiply $72$ by $32$ .

$\sqrt{2304 \cdot 8}$

Multiply $2304$ by $8$ .

$\sqrt{18432}$

$\sqrt{18432}$

Step 4

Rewrite $18432$ as $96^{2} \cdot 2$ .

Factor $9216$ out of $18432$ .

$\sqrt{9216 (2)}$

Rewrite $9216$ as $96^{2}$ .

$\sqrt{96^{2} \cdot 2}$

$\sqrt{96^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$96 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$96 \sqrt{2}$

Decimal Form:

$135.76450198 \dots$

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