Simplify 2(7 square root of 50+2 square root of 8)

$2 (7 \sqrt{50} + 2 \sqrt{8})$

Step 1

Simplify each term.

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

Factor $25$ out of $50$ .

$2 (7 \sqrt{25 (2)} + 2 \sqrt{8})$

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

$2 (7 \sqrt{5^{2} \cdot 2} + 2 \sqrt{8})$

$2 (7 \sqrt{5^{2} \cdot 2} + 2 \sqrt{8})$

Pull terms out from under the radical.

$2 (7 (5 \sqrt{2}) + 2 \sqrt{8})$

Multiply $5$ by $7$ .

$2 (35 \sqrt{2} + 2 \sqrt{8})$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$2 (35 \sqrt{2} + 2 \sqrt{4 (2)})$

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

$2 (35 \sqrt{2} + 2 \sqrt{2^{2} \cdot 2})$

$2 (35 \sqrt{2} + 2 \sqrt{2^{2} \cdot 2})$

Pull terms out from under the radical.

$2 (35 \sqrt{2} + 2 (2 \sqrt{2}))$

Multiply $2$ by $2$ .

$2 (35 \sqrt{2} + 4 \sqrt{2})$

$2 (35 \sqrt{2} + 4 \sqrt{2})$

Step 2

Simplify by adding terms.

Add $35 \sqrt{2}$ and $4 \sqrt{2}$ .

$2 (39 \sqrt{2})$

Multiply $39$ by $2$ .

$78 \sqrt{2}$

$78 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$78 \sqrt{2}$

Decimal Form:

$110.30865786 \dots$

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