Precalculus Examples

$2 i + 2 j$

Step 1

The length of the vector is the square root of the quantity of the $i$ coordinate squared plus the $j$ coordinate squared.

$\sqrt{{(2)}^{2} + {(2)}^{2}}$

Step 2

Evaluate the square root.

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Step 2.1

Raise $2$ to the power of $2$ .

$\sqrt{4 + {(2)}^{2}}$

Step 2.2

Raise $2$ to the power of $2$ .

$\sqrt{4 + 4}$

Step 2.3

Add $4$ and $4$ .

$\sqrt{8}$

Step 2.4

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

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Step 2.4.1

Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

Step 2.4.2

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

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

Step 2.5

Pull terms out from under the radical.

$2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$