Algebra Examples

$\sqrt{20 x + 20} + \sqrt{5 x + 5}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $20$ out of $20 x$ .

$\sqrt{20 (x) + 20} + \sqrt{5 x + 5}$

Step 1.1.2

Factor $20$ out of $20$ .

$\sqrt{20 (x) + 20 (1)} + \sqrt{5 x + 5}$

Step 1.1.3

Factor $20$ out of $20 (x) + 20 (1)$ .

$\sqrt{20 (x + 1)} + \sqrt{5 x + 5}$

Step 1.2

Rewrite $20 (x + 1)$ as $2^{2} \cdot (5 (x + 1^{2}))$ .

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Step 1.2.1

Factor $4$ out of $20$ .

$\sqrt{4 (5) (x + 1)} + \sqrt{5 x + 5}$

Step 1.2.2

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

$\sqrt{2^{2} \cdot 5 (x + 1)} + \sqrt{5 x + 5}$

Step 1.2.3

Rewrite $1$ as $1^{2}$ .

$\sqrt{2^{2} \cdot 5 (x + 1^{2})} + \sqrt{5 x + 5}$

Step 1.2.4

Add parentheses.

$\sqrt{2^{2} \cdot (5 (x + 1^{2}))} + \sqrt{5 x + 5}$

Step 1.3

Pull terms out from under the radical.

$2 \sqrt{5 (x + 1^{2})} + \sqrt{5 x + 5}$

Step 1.4

One to any power is one.

$2 \sqrt{5 (x + 1)} + \sqrt{5 x + 5}$

Step 1.5

Factor $5$ out of $5 x + 5$ .

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Step 1.5.1

Factor $5$ out of $5 x$ .

$2 \sqrt{5 (x + 1)} + \sqrt{5 (x) + 5}$

Step 1.5.2

Factor $5$ out of $5$ .

$2 \sqrt{5 (x + 1)} + \sqrt{5 (x) + 5 (1)}$

Step 1.5.3

Factor $5$ out of $5 (x) + 5 (1)$ .

$2 \sqrt{5 (x + 1)} + \sqrt{5 (x + 1)}$

Step 2

Add $2 \sqrt{5 (x + 1)}$ and $\sqrt{5 (x + 1)}$ .

$3 \sqrt{5 (x + 1)}$