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Evaluate -8 square root of 125-2 square root of 5-4 square root of 2

$- 8 \sqrt{125} - 2 \sqrt{5} - 4 \sqrt{2}$

Step 1

Simplify each term.

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

Factor $25$ out of $125$ .

$- 8 \sqrt{25 (5)} - 2 \sqrt{5} - 4 \sqrt{2}$

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

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

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

Pull terms out from under the radical.

$- 8 (5 \sqrt{5}) - 2 \sqrt{5} - 4 \sqrt{2}$

Multiply $5$ by $- 8$ .

$- 40 \sqrt{5} - 2 \sqrt{5} - 4 \sqrt{2}$

$- 40 \sqrt{5} - 2 \sqrt{5} - 4 \sqrt{2}$

Step 2

Subtract $2 \sqrt{5}$ from $- 40 \sqrt{5}$ .

$- 42 \sqrt{5} - 4 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 42 \sqrt{5} - 4 \sqrt{2}$

Decimal Form:

$- 99.57170930 \dots$

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