Examples

6 i + 8 j

$6 i + 8 j$

Step 1

The length of the vector is the square root of the quantity of the

i

$i$ coordinate squared plus the

j

$j$ coordinate squared.

\sqrt{{(6)}^{2} + {(8)}^{2}}

$\sqrt{{(6)}^{2} + {(8)}^{2}}$

Step 2

Evaluate the square root.

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Step 2.1

Raise

6

$6$ to the power of

2

$2$ .

\sqrt{36 + {(8)}^{2}}

$\sqrt{36 + {(8)}^{2}}$

Step 2.2

Raise

8

$8$ to the power of

2

$2$ .

\sqrt{36 + 64}

$\sqrt{36 + 64}$

Step 2.3

Add

36

$36$ and

64

$64$ .

\sqrt{100}

$\sqrt{100}$

Step 2.4

Rewrite

100

$100$ as

10^{2}

$10^{2}$ .

\sqrt{10^{2}}

$\sqrt{10^{2}}$

Step 2.5

Pull terms out from under the radical, assuming positive real numbers.

10

$10$

10

$10$

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