Algebra Examples

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

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

Step 1

Apply the distributive property.

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

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

Step 2

Multiply

\sqrt{3 x} \sqrt{3}

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

Tap for more steps...

Step 2.1

Combine using the product rule for radicals.

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

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

Step 2.2

Multiply

3

$3$ by

3

$3$ .

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

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

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

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

Step 3

Rewrite using the commutative property of multiplication.

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

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

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

Step 4.2

Pull terms out from under the radical.

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

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

Step 4.3

Multiply

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

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

Tap for more steps...

Step 4.3.1

Combine using the product rule for radicals.

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

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

Step 4.3.2

Raise

x

$x$ to the power of

1

$1$ .

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

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

Step 4.3.3

Raise

x

$x$ to the power of

1

$1$ .

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

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 4.3.5

Add

1

$1$ and

1

$1$ .

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

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

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

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

Step 4.4

Reorder

3

$3$ and

x^{2}

$x^{2}$ .

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

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

Step 4.5

Pull terms out from under the radical.

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

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

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

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

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$