Evaluate 5 square root of 8+2 square root of 20- square root of 8

$5 \sqrt{8} + 2 \sqrt{20} - \sqrt{8}$

Step 1

Simplify each term.

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

Factor $4$ out of $8$ .

$5 \sqrt{4 (2)} + 2 \sqrt{20} - \sqrt{8}$

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

$5 \sqrt{2^{2} \cdot 2} + 2 \sqrt{20} - \sqrt{8}$

$5 \sqrt{2^{2} \cdot 2} + 2 \sqrt{20} - \sqrt{8}$

Pull terms out from under the radical.

$5 (2 \sqrt{2}) + 2 \sqrt{20} - \sqrt{8}$

Multiply $2$ by $5$ .

$10 \sqrt{2} + 2 \sqrt{20} - \sqrt{8}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$10 \sqrt{2} + 2 \sqrt{4 (5)} - \sqrt{8}$

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

$10 \sqrt{2} + 2 \sqrt{2^{2} \cdot 5} - \sqrt{8}$

$10 \sqrt{2} + 2 \sqrt{2^{2} \cdot 5} - \sqrt{8}$

Pull terms out from under the radical.

$10 \sqrt{2} + 2 (2 \sqrt{5}) - \sqrt{8}$

Multiply $2$ by $2$ .

$10 \sqrt{2} + 4 \sqrt{5} - \sqrt{8}$

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

Factor $4$ out of $8$ .

$10 \sqrt{2} + 4 \sqrt{5} - \sqrt{4 (2)}$

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

$10 \sqrt{2} + 4 \sqrt{5} - \sqrt{2^{2} \cdot 2}$

$10 \sqrt{2} + 4 \sqrt{5} - \sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$10 \sqrt{2} + 4 \sqrt{5} - (2 \sqrt{2})$

Multiply $2$ by $- 1$ .

$10 \sqrt{2} + 4 \sqrt{5} - 2 \sqrt{2}$

$10 \sqrt{2} + 4 \sqrt{5} - 2 \sqrt{2}$

Step 2

Subtract $2 \sqrt{2}$ from $10 \sqrt{2}$ .

$8 \sqrt{2} + 4 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{2} + 4 \sqrt{5}$

Decimal Form:

$20.25798040 \dots$

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