Algebra Examples

$\sqrt{3 x} (\sqrt{3} - \sqrt{x})$

Step 1

Apply the distributive property.

$\sqrt{3 x} \sqrt{3} + \sqrt{3 x} (- \sqrt{x})$

Step 2

Multiply $\sqrt{3 x} \sqrt{3}$ .

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Step 2.1

Combine using the product rule for radicals.

$\sqrt{3 x \cdot 3} + \sqrt{3 x} (- \sqrt{x})$

Step 2.2

Multiply $3$ by $3$ .

$\sqrt{9 x} + \sqrt{3 x} (- \sqrt{x})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{9 x} - \sqrt{3 x} \sqrt{x}$

Step 4

Simplify each term.

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Step 4.1

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

$\sqrt{3^{2} x} - \sqrt{3 x} \sqrt{x}$

Step 4.2

Pull terms out from under the radical.

$3 \sqrt{x} - \sqrt{3 x} \sqrt{x}$

Step 4.3

Multiply $- \sqrt{3 x} \sqrt{x}$ .

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Step 4.3.1

Combine using the product rule for radicals.

$3 \sqrt{x} - \sqrt{x (3 x)}$

Step 4.3.2

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

$3 \sqrt{x} - \sqrt{3 (x^{1} x)}$

Step 4.3.3

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

$3 \sqrt{x} - \sqrt{3 (x^{1} x^{1})}$

Step 4.3.4

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

$3 \sqrt{x} - \sqrt{3 x^{1 + 1}}$

Step 4.3.5

Add $1$ and $1$ .

$3 \sqrt{x} - \sqrt{3 x^{2}}$

Step 4.4

Reorder $3$ and $x^{2}$ .

$3 \sqrt{x} - \sqrt{x^{2} \cdot 3}$

Step 4.5

Pull terms out from under the radical.

$3 \sqrt{x} - x \sqrt{3}$