Algebra Examples

$12 i - 9 j$

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

$l = \sqrt{{(12)}^{2} + {(- 9)}^{2}}$

Evaluate the square root.

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Remove parentheses around $12$ .

$l = \sqrt{12^{2} + {(- 9)}^{2}}$

Raise $12$ to the power of $2$ to get $144$ .

$l = \sqrt{144 + {(- 9)}^{2}}$

Raise $- 9$ to the power of $2$ to get $81$ .

$l = \sqrt{144 + 81}$

Add $144$ and $81$ to get $225$ .

$l = \sqrt{225}$

Rewrite $225$ as $15^{2}$ .

$l = \sqrt{15^{2}}$

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

$l = 15$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]