Simplify - square root of 2*5 square root of 20

$- \sqrt{2} \cdot 5 \sqrt{20}$

Step 1

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

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

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

$- \sqrt{2} \cdot (5 \sqrt{2^{2} \cdot 5})$

$- \sqrt{2} \cdot (5 \sqrt{2^{2} \cdot 5})$

Step 2

Pull terms out from under the radical.

$- \sqrt{2} \cdot (5 (2 \sqrt{5}))$

Step 3

Multiply $2$ by $5$ .

$- \sqrt{2} \cdot (10 \sqrt{5})$

Step 4

Multiply $- \sqrt{2} (10 \sqrt{5})$ .

Multiply $10$ by $- 1$ .

$- 10 \sqrt{2} \sqrt{5}$

Combine using the product rule for radicals.

$- 10 \sqrt{5 \cdot 2}$

Multiply $5$ by $2$ .

$- 10 \sqrt{10}$

$- 10 \sqrt{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 10 \sqrt{10}$

Decimal Form:

$- 31.62277660 \dots$

Related Questions