Simplify (2 square root of 8+3 square root of 5)

$(2 \sqrt{8} + 3 \sqrt{5})$

Step 1

Remove parentheses.

$2 \sqrt{8} + 3 \sqrt{5}$

Step 2

Simplify each term.

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

Factor $4$ out of $8$ .

$2 \sqrt{4 (2)} + 3 \sqrt{5}$

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

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

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

Pull terms out from under the radical.

$2 (2 \sqrt{2}) + 3 \sqrt{5}$

Multiply $2$ by $2$ .

$4 \sqrt{2} + 3 \sqrt{5}$

$4 \sqrt{2} + 3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{2} + 3 \sqrt{5}$

Decimal Form:

$12.36505818 \dots$

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