Algebra Examples

$2 i + 2 j$

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

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

Evaluate the square root.

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Remove parentheses around $2$ .

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

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

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

Remove parentheses around $2$ .

$l = \sqrt{4 + 2^{2}}$

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

$l = \sqrt{4 + 4}$

Add $4$ and $4$ .

$l = \sqrt{8}$

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

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Factor $4$ out of $8$ .

$l = \sqrt{4 (2)}$

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

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

Pull terms out from under the radical.

$l = 2 \sqrt{2}$

The result can be shown in both exact and decimal forms.

Exact Form:

$l = 2 \sqrt{2}$

Decimal Form:

$l = 2.82842712 \dots$

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