Simplify 3 square root of 50* square root of 22

$3 \sqrt{50} \cdot \sqrt{22}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$3 \sqrt{25 (2)} \cdot \sqrt{22}$

Rewrite $25$ as $5^{2}$ .

$3 \sqrt{5^{2} \cdot 2} \cdot \sqrt{22}$

$3 \sqrt{5^{2} \cdot 2} \cdot \sqrt{22}$

Pull terms out from under the radical.

$3 (5 \sqrt{2}) \cdot \sqrt{22}$

Multiply $5$ by $3$ .

$15 \sqrt{2} \cdot \sqrt{22}$

Multiply $15 \sqrt{2} \sqrt{22}$ .

Combine using the product rule for radicals.

$15 \sqrt{22 \cdot 2}$

Multiply $22$ by $2$ .

$15 \sqrt{44}$

$15 \sqrt{44}$

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

Factor $4$ out of $44$ .

$15 \sqrt{4 (11)}$

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

$15 \sqrt{2^{2} \cdot 11}$

$15 \sqrt{2^{2} \cdot 11}$

Pull terms out from under the radical.

$15 (2 \sqrt{11})$

Multiply $2$ by $15$ .

$30 \sqrt{11}$

The result can be shown in multiple forms.

Exact Form:

$30 \sqrt{11}$

Decimal Form:

$99.49874371 \dots$

Related Questions