Simplify |3-6i|

$| 3 - 6 i |$

Step 1

Use the formula $| a + b i | = \sqrt{a^{2} + b^{2}}$ to find the magnitude.

$\sqrt{3^{2} + {(- 6)}^{2}}$

Step 2

Raise $3$ to the power of $2$ .

$\sqrt{9 + {(- 6)}^{2}}$

Step 3

Raise $- 6$ to the power of $2$ .

$\sqrt{9 + 36}$

Step 4

Add $9$ and $36$ .

$\sqrt{45}$

Step 5

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

$3 \sqrt{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$