Evaluate 8 square root of 5- square root of 45- square root of 80

$8 \sqrt{5} - \sqrt{45} - \sqrt{80}$

Step 1

Simplify each term.

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

Factor $9$ out of $45$ .

$8 \sqrt{5} - \sqrt{9 (5)} - \sqrt{80}$

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

$8 \sqrt{5} - \sqrt{3^{2} \cdot 5} - \sqrt{80}$

$8 \sqrt{5} - \sqrt{3^{2} \cdot 5} - \sqrt{80}$

Pull terms out from under the radical.

$8 \sqrt{5} - (3 \sqrt{5}) - \sqrt{80}$

Multiply $3$ by $- 1$ .

$8 \sqrt{5} - 3 \sqrt{5} - \sqrt{80}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$8 \sqrt{5} - 3 \sqrt{5} - \sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

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

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

Pull terms out from under the radical.

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

Multiply $4$ by $- 1$ .

$8 \sqrt{5} - 3 \sqrt{5} - 4 \sqrt{5}$

$8 \sqrt{5} - 3 \sqrt{5} - 4 \sqrt{5}$

Step 2

Simplify by adding terms.

Subtract $3 \sqrt{5}$ from $8 \sqrt{5}$ .

$5 \sqrt{5} - 4 \sqrt{5}$

Subtract $4 \sqrt{5}$ from $5 \sqrt{5}$ .

$\sqrt{5}$

$\sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$

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