Finite Math Examples

$\sqrt{27 x} + \sqrt{12 x} - \sqrt{3 x}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $27$ .

$\sqrt{9 (3) x} + \sqrt{12 x} - \sqrt{3 x}$

Step 1.1.2

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

$\sqrt{3^{2} \cdot 3 x} + \sqrt{12 x} - \sqrt{3 x}$

Step 1.1.3

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{3 x} + \sqrt{12 x} - \sqrt{3 x}$

Step 1.3

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

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Step 1.3.1

Factor $4$ out of $12$ .

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

Step 1.3.2

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

$3 \sqrt{3 x} + \sqrt{2^{2} \cdot 3 x} - \sqrt{3 x}$

Step 1.3.3

Add parentheses.

$3 \sqrt{3 x} + \sqrt{2^{2} \cdot (3 x)} - \sqrt{3 x}$

Step 1.4

Pull terms out from under the radical.

$3 \sqrt{3 x} + 2 \sqrt{3 x} - \sqrt{3 x}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $3 \sqrt{3 x}$ and $2 \sqrt{3 x}$ .

$5 \sqrt{3 x} - \sqrt{3 x}$

Step 2.2

Subtract $\sqrt{3 x}$ from $5 \sqrt{3 x}$ .

$4 \sqrt{3 x}$