Algebra Examples

$(\sqrt{18 x} + 4 \sqrt{8 x} - \sqrt{50 x})$

Step 1

Remove parentheses.

$\sqrt{18 x} + 4 \sqrt{8 x} - \sqrt{50 x}$

Step 2

Simplify each term.

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Step 2.1

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

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Step 2.1.1

Factor $9$ out of $18$ .

$\sqrt{9 (2) x} + 4 \sqrt{8 x} - \sqrt{50 x}$

Step 2.1.2

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

$\sqrt{3^{2} \cdot 2 x} + 4 \sqrt{8 x} - \sqrt{50 x}$

Step 2.1.3

Add parentheses.

$\sqrt{3^{2} \cdot (2 x)} + 4 \sqrt{8 x} - \sqrt{50 x}$

Step 2.2

Pull terms out from under the radical.

$3 \sqrt{2 x} + 4 \sqrt{8 x} - \sqrt{50 x}$

Step 2.3

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

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Step 2.3.1

Factor $4$ out of $8$ .

$3 \sqrt{2 x} + 4 \sqrt{4 (2) x} - \sqrt{50 x}$

Step 2.3.2

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

$3 \sqrt{2 x} + 4 \sqrt{2^{2} \cdot 2 x} - \sqrt{50 x}$

Step 2.3.3

Add parentheses.

$3 \sqrt{2 x} + 4 \sqrt{2^{2} \cdot (2 x)} - \sqrt{50 x}$

Step 2.4

Pull terms out from under the radical.

$3 \sqrt{2 x} + 4 (2 \sqrt{2 x}) - \sqrt{50 x}$

Step 2.5

Multiply $2$ by $4$ .

$3 \sqrt{2 x} + 8 \sqrt{2 x} - \sqrt{50 x}$

Step 2.6

Rewrite $50 x$ as $5^{2} \cdot (2 x)$ .

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Step 2.6.1

Factor $25$ out of $50$ .

$3 \sqrt{2 x} + 8 \sqrt{2 x} - \sqrt{25 (2) x}$

Step 2.6.2

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

$3 \sqrt{2 x} + 8 \sqrt{2 x} - \sqrt{5^{2} \cdot 2 x}$

Step 2.6.3

Add parentheses.

$3 \sqrt{2 x} + 8 \sqrt{2 x} - \sqrt{5^{2} \cdot (2 x)}$

Step 2.7

Pull terms out from under the radical.

$3 \sqrt{2 x} + 8 \sqrt{2 x} - (5 \sqrt{2 x})$

Step 2.8

Multiply $5$ by $- 1$ .

$3 \sqrt{2 x} + 8 \sqrt{2 x} - 5 \sqrt{2 x}$

Step 3

Simplify by adding terms.

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Step 3.1

Add $3 \sqrt{2 x}$ and $8 \sqrt{2 x}$ .

$11 \sqrt{2 x} - 5 \sqrt{2 x}$

Step 3.2

Subtract $5 \sqrt{2 x}$ from $11 \sqrt{2 x}$ .

$6 \sqrt{2 x}$