Simplify 5 square root of 32

$5 \sqrt{32}$

Step 1

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

Factor $16$ out of $32$ .

$5 \sqrt{16 (2)}$

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

$5 \sqrt{4^{2} \cdot 2}$

$5 \sqrt{4^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$5 (4 \sqrt{2})$

Step 3

Multiply $4$ by $5$ .

$20 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$20 \sqrt{2}$

Decimal Form:

$28.28427124 \dots$

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