Simplify the Radical Expression 8 square root of 5*5 square root of 10

$8 \sqrt{5} \cdot 5 \sqrt{10}$

Step 1

Multiply $5$ by $8$ .

$40 \sqrt{5} \sqrt{10}$

Step 2

Multiply $40 \sqrt{5} \sqrt{10}$ .

Combine using the product rule for radicals.

$40 \sqrt{10 \cdot 5}$

Multiply $10$ by $5$ .

$40 \sqrt{50}$

Step 3

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$40 \sqrt{25 (2)}$

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

$40 \sqrt{5^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$40 (| 5 | \sqrt{2})$

Step 5

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$40 (5 \sqrt{2})$

Step 6

Multiply $5$ by $40$ .

$200 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$200 \sqrt{2}$

Decimal Form:

$282.84271247 \dots$