Find the Exact Value |7-i|

$| 7 - i |$

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

$\sqrt{7^{2} + {(- 1)}^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{49 + {(- 1)}^{2}}$

Raise $- 1$ to the power of $2$ .

$\sqrt{49 + 1}$

Add $49$ and $1$ .

$\sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

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

Pull terms out from under the radical.

$5 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$