Simplify ( square root of 22)(5 square root of 2)

$(\sqrt{22}) (5 \sqrt{2})$

Multiply $(\sqrt{22}) (5 \sqrt{2})$ .

Combine using the product rule for radicals.

$5 \sqrt{22 \cdot 2}$

Multiply $22$ by $2$ .

$5 \sqrt{44}$

$5 \sqrt{44}$

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$5 \sqrt{4 (11)}$

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

$5 \sqrt{2^{2} \cdot 11}$

$5 \sqrt{2^{2} \cdot 11}$

Pull terms out from under the radical.

$5 (2 \sqrt{11})$

Multiply $2$ by $5$ .

$10 \sqrt{11}$

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{11}$

Decimal Form:

$33.16624790 \dots$

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