Evaluate 8 square root of 48-6 square root of 75+7 square root of 80

$8 \sqrt{48} - 6 \sqrt{75} + 7 \sqrt{80}$

Step 1

Simplify each term.

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$8 \sqrt{16 (3)} - 6 \sqrt{75} + 7 \sqrt{80}$

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

$8 \sqrt{4^{2} \cdot 3} - 6 \sqrt{75} + 7 \sqrt{80}$

Pull terms out from under the radical.

$8 (4 \sqrt{3}) - 6 \sqrt{75} + 7 \sqrt{80}$

Multiply $4$ by $8$ .

$32 \sqrt{3} - 6 \sqrt{75} + 7 \sqrt{80}$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$32 \sqrt{3} - 6 \sqrt{25 (3)} + 7 \sqrt{80}$

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

$32 \sqrt{3} - 6 \sqrt{5^{2} \cdot 3} + 7 \sqrt{80}$

Pull terms out from under the radical.

$32 \sqrt{3} - 6 (5 \sqrt{3}) + 7 \sqrt{80}$

Multiply $5$ by $- 6$ .

$32 \sqrt{3} - 30 \sqrt{3} + 7 \sqrt{80}$

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

Factor $16$ out of $80$ .

$32 \sqrt{3} - 30 \sqrt{3} + 7 \sqrt{16 (5)}$

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

$32 \sqrt{3} - 30 \sqrt{3} + 7 \sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$32 \sqrt{3} - 30 \sqrt{3} + 7 (4 \sqrt{5})$

Multiply $4$ by $7$ .

$32 \sqrt{3} - 30 \sqrt{3} + 28 \sqrt{5}$

Step 2

Subtract $30 \sqrt{3}$ from $32 \sqrt{3}$ .

$2 \sqrt{3} + 28 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3} + 28 \sqrt{5}$

Decimal Form:

$66.07400498 \dots$