Algebra Examples

$\sqrt{2} \cdot 0.5 \sqrt{8}$

Step 1

Multiply $\sqrt{2}$ by $0.5$ .

$0.70710678 \sqrt{8}$

Step 2

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 2.1

Factor $4$ out of $8$ .

$0.70710678 \sqrt{4 (2)}$

Step 2.2

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

$0.70710678 \sqrt{2^{2} \cdot 2}$

Step 3

Pull terms out from under the radical.

$0.70710678 (| 2 | \sqrt{2})$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$0.70710678 (2 \sqrt{2})$

Step 5

Multiply $0.70710678 (2 \sqrt{2})$ .

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Step 5.1

Multiply $2$ by $0.70710678$ .

$1.41421356 \sqrt{2}$

Step 5.2

Multiply $1.41421356$ by $\sqrt{2}$ .

$2$