Precalculus Examples

$v = - 4 i + 5 j$

Step 1

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

$\sqrt{{(- 4)}^{2} + {(5)}^{2}}$

Step 2

Evaluate the square root.

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Step 2.1

Raise $- 4$ to the power of $2$ .

$\sqrt{16 + {(5)}^{2}}$

Step 2.2

Raise $5$ to the power of $2$ .

$\sqrt{16 + 25}$

Step 2.3

Add $16$ and $25$ .

$\sqrt{41}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{41}$

Decimal Form:

$6.40312423 \dots$