Algebra Examples

$\sqrt{3} (\sqrt{27} - \sqrt{3})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $27$ as $3^{2} \cdot 3$ .

Tap for more steps...

Step 1.1.1

Factor $9$ out of $27$ .

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

Step 1.1.2

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

$\sqrt{3} (\sqrt{3^{2} \cdot 3} - \sqrt{3})$

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

Step 2

Subtract $\sqrt{3}$ from $3 \sqrt{3}$ .

$\sqrt{3} (2 \sqrt{3})$

Step 3

Multiply $\sqrt{3} (2 \sqrt{3})$ .

Tap for more steps...

Step 3.1

Raise $\sqrt{3}$ to the power of $1$ .

$2 ({\sqrt{3}}^{1} \sqrt{3})$

Step 3.2

Raise $\sqrt{3}$ to the power of $1$ .

$2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 3.3

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

$2 {\sqrt{3}}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

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

Step 4

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$2 {(3^{\frac{1}{2}})}^{2}$

Step 4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 4.3

Combine $\frac{1}{2}$ and $2$ .

$2 \cdot 3^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.4.1

Cancel the common factor.

$2 \cdot 3^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

$2 \cdot 3^{1}$

Step 4.5

Evaluate the exponent.

$2 \cdot 3$

Step 5

Multiply $2$ by $3$ .

$6$