Algebra Examples

$3 \sqrt{27 u} - 2 \sqrt{12 u}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $27 u$ as $3^{2} \cdot (3 u)$ .

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Step 1.1.1

Factor $9$ out of $27$ .

$3 \sqrt{9 (3) u} - 2 \sqrt{12 u}$

Step 1.1.2

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

$3 \sqrt{3^{2} \cdot 3 u} - 2 \sqrt{12 u}$

Step 1.1.3

Add parentheses.

$3 \sqrt{3^{2} \cdot (3 u)} - 2 \sqrt{12 u}$

$3 \sqrt{3^{2} \cdot (3 u)} - 2 \sqrt{12 u}$

Step 1.2

Pull terms out from under the radical.

$3 (3 \sqrt{3 u}) - 2 \sqrt{12 u}$

Step 1.3

Multiply $3$ by $3$ .

$9 \sqrt{3 u} - 2 \sqrt{12 u}$

Step 1.4

Rewrite $12 u$ as $2^{2} \cdot (3 u)$ .

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Step 1.4.1

Factor $4$ out of $12$ .

$9 \sqrt{3 u} - 2 \sqrt{4 (3) u}$

Step 1.4.2

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

$9 \sqrt{3 u} - 2 \sqrt{2^{2} \cdot 3 u}$

Step 1.4.3

Add parentheses.

$9 \sqrt{3 u} - 2 \sqrt{2^{2} \cdot (3 u)}$

$9 \sqrt{3 u} - 2 \sqrt{2^{2} \cdot (3 u)}$

Step 1.5

Pull terms out from under the radical.

$9 \sqrt{3 u} - 2 (2 \sqrt{3 u})$

Step 1.6

Multiply $2$ by $- 2$ .

$9 \sqrt{3 u} - 4 \sqrt{3 u}$

$9 \sqrt{3 u} - 4 \sqrt{3 u}$

Step 2

Subtract $4 \sqrt{3 u}$ from $9 \sqrt{3 u}$ .

$5 \sqrt{3 u}$

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