Algebra Examples

$\frac{1}{2} \sqrt{4 x} - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $4$ as $2^{2}$ .

$\frac{1}{2} \sqrt{2^{2} x} - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Step 1.2

Pull terms out from under the radical.

$\frac{1}{2} (| 2 | \sqrt{x}) - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Step 1.3

Remove non-negative terms from the absolute value.

$\frac{1}{2} (2 \sqrt{x}) - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $2 \sqrt{x}$ .

$\frac{1}{2} (2 (\sqrt{x})) - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Step 1.4.2

Cancel the common factor.

$\frac{1}{2} (2 \sqrt{x}) - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Step 1.4.3

Rewrite the expression.

$\sqrt{x} - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Step 1.5

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

$\sqrt{x} - \frac{1}{3} \sqrt{3^{2} x} + \frac{1}{4} \sqrt{64}$

Step 1.6

Pull terms out from under the radical.

$\sqrt{x} - \frac{1}{3} (| 3 | \sqrt{x}) + \frac{1}{4} \sqrt{64}$

Step 1.7

Remove non-negative terms from the absolute value.

$\sqrt{x} - \frac{1}{3} (3 \sqrt{x}) + \frac{1}{4} \sqrt{64}$

Step 1.8

Cancel the common factor of $3$ .

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Step 1.8.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\sqrt{x} + \frac{- 1}{3} (3 \sqrt{x}) + \frac{1}{4} \sqrt{64}$

Step 1.8.2

Factor $3$ out of $3 \sqrt{x}$ .

$\sqrt{x} + \frac{- 1}{3} (3 (\sqrt{x})) + \frac{1}{4} \sqrt{64}$

Step 1.8.3

Cancel the common factor.

$\sqrt{x} + \frac{- 1}{3} (3 \sqrt{x}) + \frac{1}{4} \sqrt{64}$

Step 1.8.4

Rewrite the expression.

$\sqrt{x} - 1 \sqrt{x} + \frac{1}{4} \sqrt{64}$

Step 1.9

Rewrite $- 1 \sqrt{x}$ as $- \sqrt{x}$ .

$\sqrt{x} - \sqrt{x} + \frac{1}{4} \sqrt{64}$

Step 1.10

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

$\sqrt{x} - \sqrt{x} + \frac{1}{4} \sqrt{8^{2}}$

Step 1.11

Pull terms out from under the radical.

$\sqrt{x} - \sqrt{x} + \frac{1}{4} | 8 |$

Step 1.12

Remove non-negative terms from the absolute value.

$\sqrt{x} - \sqrt{x} + \frac{1}{4} \cdot 8$

Step 1.13

Cancel the common factor of $4$ .

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Step 1.13.1

Factor $4$ out of $8$ .

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

Step 1.13.2

Cancel the common factor.

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

Step 1.13.3

Rewrite the expression.

$\sqrt{x} - \sqrt{x} + 2$

Step 2

Subtract $\sqrt{x}$ from $\sqrt{x}$ .

$0 + 2$

Step 3

Add $0$ and $2$ .

$2$