Algebra Examples

$\sqrt{45 x^{2} + 9 x^{3}} + 2 x \sqrt{20 + 4 x} + \sqrt{5 x^{2} + x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Factor $9 x^{2}$ out of $45 x^{2} + 9 x^{3}$ .

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Step 1.1.1

Factor $9 x^{2}$ out of $45 x^{2}$ .

$\sqrt{9 x^{2} (5) + 9 x^{3}} + 2 x \sqrt{20 + 4 x} + \sqrt{5 x^{2} + x^{3}}$

Step 1.1.2

Factor $9 x^{2}$ out of $9 x^{3}$ .

$\sqrt{9 x^{2} (5) + 9 x^{2} (x)} + 2 x \sqrt{20 + 4 x} + \sqrt{5 x^{2} + x^{3}}$

Step 1.1.3

Factor $9 x^{2}$ out of $9 x^{2} (5) + 9 x^{2} (x)$ .

$\sqrt{9 x^{2} (5 + x)} + 2 x \sqrt{20 + 4 x} + \sqrt{5 x^{2} + x^{3}}$

Step 1.2

Rewrite $9 x^{2} (5 + x)$ as ${(3 x)}^{2} (5 + x)$ .

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Step 1.2.1

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

$\sqrt{3^{2} x^{2} (5 + x)} + 2 x \sqrt{20 + 4 x} + \sqrt{5 x^{2} + x^{3}}$

Step 1.2.2

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

$\sqrt{{(3 x)}^{2} (5 + x)} + 2 x \sqrt{20 + 4 x} + \sqrt{5 x^{2} + x^{3}}$

Step 1.3

Pull terms out from under the radical.

$3 x \sqrt{5 + x} + 2 x \sqrt{20 + 4 x} + \sqrt{5 x^{2} + x^{3}}$

Step 1.4

Factor $4$ out of $20 + 4 x$ .

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Step 1.4.1

Factor $4$ out of $20$ .

$3 x \sqrt{5 + x} + 2 x \sqrt{4 \cdot 5 + 4 x} + \sqrt{5 x^{2} + x^{3}}$

Step 1.4.2

Factor $4$ out of $4 \cdot 5 + 4 x$ .

$3 x \sqrt{5 + x} + 2 x \sqrt{4 (5 + x)} + \sqrt{5 x^{2} + x^{3}}$

Step 1.5

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

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

Step 1.6

Pull terms out from under the radical.

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

Step 1.7

Multiply $2$ by $2$ .

$3 x \sqrt{5 + x} + 4 x \sqrt{5 + x} + \sqrt{5 x^{2} + x^{3}}$

Step 1.8

Factor $x^{2}$ out of $5 x^{2} + x^{3}$ .

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Step 1.8.1

Factor $x^{2}$ out of $5 x^{2}$ .

$3 x \sqrt{5 + x} + 4 x \sqrt{5 + x} + \sqrt{x^{2} \cdot 5 + x^{3}}$

Step 1.8.2

Factor $x^{2}$ out of $x^{3}$ .

$3 x \sqrt{5 + x} + 4 x \sqrt{5 + x} + \sqrt{x^{2} \cdot 5 + x^{2} x}$

Step 1.8.3

Factor $x^{2}$ out of $x^{2} \cdot 5 + x^{2} x$ .

$3 x \sqrt{5 + x} + 4 x \sqrt{5 + x} + \sqrt{x^{2} (5 + x)}$

Step 1.9

Pull terms out from under the radical.

$3 x \sqrt{5 + x} + 4 x \sqrt{5 + x} + x \sqrt{5 + x}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $3 x \sqrt{5 + x}$ and $4 x \sqrt{5 + x}$ .

$7 x \sqrt{5 + x} + x \sqrt{5 + x}$

Step 2.2

Add $7 x \sqrt{5 + x}$ and $x \sqrt{5 + x}$ .

$8 x \sqrt{5 + x}$