Algebra Examples

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

Step 1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.1

Factor $16$ out of $32$ .

$\sqrt{8 \sqrt{16 (2)}}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{8 \sqrt{4^{2} \cdot 2}}$

$\sqrt{8 \sqrt{4^{2} \cdot 2}}$

Step 2

Pull terms out from under the radical.

$\sqrt{8 \cdot 4 \sqrt{2}}$

Step 3

Multiply $8$ by $4$ .

$\sqrt{32 \sqrt{2}}$

Step 4

Rewrite $32 \sqrt{2}$ as ${(2^{2})}^{2} \cdot (2 \sqrt{2})$ .

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Step 4.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) \sqrt{2}}$

Step 4.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 \sqrt{2}}$

Step 4.3

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

$\sqrt{{(2^{2})}^{2} \cdot 2 \sqrt{2}}$

Step 4.4

Add parentheses.

$\sqrt{{(2^{2})}^{2} \cdot (2 \sqrt{2})}$

$\sqrt{{(2^{2})}^{2} \cdot (2 \sqrt{2})}$

Step 5

Pull terms out from under the radical.

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

Step 6

Raise $2$ to the power of $2$ .

$4 \sqrt{2 \sqrt{2}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{2 \sqrt{2}}$

Decimal Form:

$6.72717132 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$