Algebra Examples

$\sqrt{324} - \frac{1}{2} \sqrt{64}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $324$ as $18^{2}$ .

$\sqrt{18^{2}} - \frac{1}{2} \cdot \sqrt{64}$

Step 1.2

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

$18 - \frac{1}{2} \cdot \sqrt{64}$

Step 1.3

Rewrite $64$ as $8^{2}$ .

$18 - \frac{1}{2} \cdot \sqrt{8^{2}}$

Step 1.4

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

$18 - \frac{1}{2} \cdot 8$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$18 + \frac{- 1}{2} \cdot 8$

Step 1.5.2

Factor $2$ out of $8$ .

$18 + \frac{- 1}{2} \cdot (2 (4))$

Step 1.5.3

Cancel the common factor.

$18 + \frac{- 1}{2} \cdot (2 \cdot 4)$

Step 1.5.4

Rewrite the expression.

$18 - 1 \cdot 4$

Step 1.6

Multiply $- 1$ by $4$ .

$18 - 4$

Step 2

Subtract $4$ from $18$ .

$14$