Algebra Examples

$6 i + 8 j$

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

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

Evaluate the square root.

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Remove parentheses.

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

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

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

Remove parentheses.

$l = \sqrt{36 + 8^{2}}$

Raise $8$ to the power of $2$ .

$l = \sqrt{36 + 64}$

Add $36$ and $64$ .

$l = \sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$l = \sqrt{10^{2}}$

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

$l = 10$

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