Finite Math Examples

$\sqrt{6 x} - 2 \sqrt{54} + 5 \sqrt{150 x}$

Step 1

Rewrite $54$ as $3^{2} \cdot 6$ .

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Step 1.1

Factor $9$ out of $54$ .

$\sqrt{6 x} - 2 \sqrt{9 (6)} + 5 \sqrt{150 x}$

Step 1.2

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

$\sqrt{6 x} - 2 \sqrt{3^{2} \cdot 6} + 5 \sqrt{150 x}$

Step 2

Pull terms out from under the radical.

$\sqrt{6 x} - 2 (3 \sqrt{6}) + 5 \sqrt{150 x}$

Step 3

Multiply $3$ by $- 2$ .

$\sqrt{6 x} - 6 \sqrt{6} + 5 \sqrt{150 x}$

Step 4

Rewrite $150 x$ as $5^{2} \cdot (6 x)$ .

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Step 4.1

Factor $25$ out of $150$ .

$\sqrt{6 x} - 6 \sqrt{6} + 5 \sqrt{25 (6) x}$

Step 4.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{6 x} - 6 \sqrt{6} + 5 \sqrt{5^{2} \cdot 6 x}$

Step 4.3

Add parentheses.

$\sqrt{6 x} - 6 \sqrt{6} + 5 \sqrt{5^{2} \cdot (6 x)}$

Step 5

Pull terms out from under the radical.

$\sqrt{6 x} - 6 \sqrt{6} + 5 (5 \sqrt{6 x})$

Step 6

Multiply $5$ by $5$ .

$\sqrt{6 x} - 6 \sqrt{6} + 25 \sqrt{6 x}$

Step 7

Add $\sqrt{6 x}$ and $25 \sqrt{6 x}$ .

$26 \sqrt{6 x} - 6 \sqrt{6}$

Step 8

Factor $2$ out of $26 \sqrt{6 x} - 6 \sqrt{6}$ .

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Step 8.1

Factor $2$ out of $26 \sqrt{6 x}$ .

$2 (13 \sqrt{6 x}) - 6 \sqrt{6}$

Step 8.2

Factor $2$ out of $- 6 \sqrt{6}$ .

$2 (13 \sqrt{6 x}) + 2 (- 3 \sqrt{6})$

Step 8.3

Factor $2$ out of $2 (13 \sqrt{6 x}) + 2 (- 3 \sqrt{6})$ .

$2 (13 \sqrt{6 x} - 3 \sqrt{6})$