Examples

2 i + 2 j

$2 i + 2 j$

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{{(2)}^{2} + {(2)}^{2}}

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

Step 2

Evaluate the square root.

Tap for more steps...

Step 2.1

Raise

2

$2$ to the power of

2

$2$ .

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

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

Step 2.2

Raise

2

$2$ to the power of

2

$2$ .

\sqrt{4 + 4}

$\sqrt{4 + 4}$

Step 2.3

Add

4

$4$ and

4

$4$ .

\sqrt{8}

$\sqrt{8}$

Step 2.4

Rewrite

8

$8$ as

2^{2} \cdot 2

$2^{2} \cdot 2$ .

Tap for more steps...

Step 2.4.1

Factor

4

$4$ out of

8

$8$ .

\sqrt{4 (2)}

$\sqrt{4 (2)}$

Step 2.4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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

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

Step 2.5

Pull terms out from under the radical.

2 \sqrt{2}

$2 \sqrt{2}$

2 \sqrt{2}

$2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

2 \sqrt{2}

$2 \sqrt{2}$

Decimal Form:

2.82842712 \dots

$2.82842712 \dots$

Enter YOUR Problem