Evaluate 8 square root of 5-2 square root of 4+8 square root of 45

$8 \sqrt{5} - 2 \sqrt{4} + 8 \sqrt{45}$

Step 1

Simplify each term.

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

$8 \sqrt{5} - 2 \sqrt{2^{2}} + 8 \sqrt{45}$

Pull terms out from under the radical, assuming positive real numbers.

$8 \sqrt{5} - 2 \cdot 2 + 8 \sqrt{45}$

Multiply $- 2$ by $2$ .

$8 \sqrt{5} - 4 + 8 \sqrt{45}$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$8 \sqrt{5} - 4 + 8 \sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$8 \sqrt{5} - 4 + 8 \sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$8 \sqrt{5} - 4 + 8 (3 \sqrt{5})$

Multiply $3$ by $8$ .

$8 \sqrt{5} - 4 + 24 \sqrt{5}$

Step 2

Add $8 \sqrt{5}$ and $24 \sqrt{5}$ .

$- 4 + 32 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 4 + 32 \sqrt{5}$

Decimal Form:

$67.55417527 \dots$