Evaluate 8 square root of 125-3 square root of 12-6 square root of 45

$8 \sqrt{125} - 3 \sqrt{12} - 6 \sqrt{45}$

Step 1

Simplify each term.

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$8 \sqrt{25 (5)} - 3 \sqrt{12} - 6 \sqrt{45}$

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

$8 \sqrt{5^{2} \cdot 5} - 3 \sqrt{12} - 6 \sqrt{45}$

Pull terms out from under the radical.

$8 (5 \sqrt{5}) - 3 \sqrt{12} - 6 \sqrt{45}$

Multiply $5$ by $8$ .

$40 \sqrt{5} - 3 \sqrt{12} - 6 \sqrt{45}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$40 \sqrt{5} - 3 \sqrt{4 (3)} - 6 \sqrt{45}$

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

$40 \sqrt{5} - 3 \sqrt{2^{2} \cdot 3} - 6 \sqrt{45}$

Pull terms out from under the radical.

$40 \sqrt{5} - 3 (2 \sqrt{3}) - 6 \sqrt{45}$

Multiply $2$ by $- 3$ .

$40 \sqrt{5} - 6 \sqrt{3} - 6 \sqrt{45}$

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

Factor $9$ out of $45$ .

$40 \sqrt{5} - 6 \sqrt{3} - 6 \sqrt{9 (5)}$

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

$40 \sqrt{5} - 6 \sqrt{3} - 6 \sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$40 \sqrt{5} - 6 \sqrt{3} - 6 (3 \sqrt{5})$

Multiply $3$ by $- 6$ .

$40 \sqrt{5} - 6 \sqrt{3} - 18 \sqrt{5}$

Step 2

Subtract $18 \sqrt{5}$ from $40 \sqrt{5}$ .

$22 \sqrt{5} - 6 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$22 \sqrt{5} - 6 \sqrt{3}$

Decimal Form:

$38.80119065 \dots$