Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $8$ .

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

Step 1.1.2

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

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

Step 1.1.3

Move $2$ .

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

Step 1.1.4

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

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

Step 1.2

Pull terms out from under the radical.

$\sqrt{5 x} (2 x \sqrt{2} - 2 \sqrt{x})$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Reorder.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2.2

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $2 \sqrt{2} \sqrt{5 x}$ .

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Step 3.1.1

Combine using the product rule for radicals.

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

Step 3.1.2

Multiply $2$ by $5$ .

$2 \sqrt{10 x} x - 2 \sqrt{5 x} \sqrt{x}$

Step 3.2

Multiply $- 2 \sqrt{5 x} \sqrt{x}$ .

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Step 3.2.1

Combine using the product rule for radicals.

$2 \sqrt{10 x} x - 2 \sqrt{x (5 x)}$

Step 3.2.2

Raise $x$ to the power of $1$ .

$2 \sqrt{10 x} x - 2 \sqrt{5 (x^{1} x)}$

Step 3.2.3

Raise $x$ to the power of $1$ .

$2 \sqrt{10 x} x - 2 \sqrt{5 (x^{1} x^{1})}$

Step 3.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \sqrt{10 x} x - 2 \sqrt{5 x^{1 + 1}}$

Step 3.2.5

Add $1$ and $1$ .

$2 \sqrt{10 x} x - 2 \sqrt{5 x^{2}}$

Step 3.3

Reorder $5$ and $x^{2}$ .

$2 \sqrt{10 x} x - 2 \sqrt{x^{2} \cdot 5}$

Step 3.4

Pull terms out from under the radical.

$2 \sqrt{10 x} x - 2 x \sqrt{5}$