Pre-Algebra Examples

$\sqrt{6} (\sqrt{2} - 4 \sqrt{6} + 3 \sqrt{15})$

Step 1

Apply the distributive property.

$\sqrt{6} \sqrt{2} + \sqrt{6} (- 4 \sqrt{6}) + \sqrt{6} (3 \sqrt{15})$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Combine using the product rule for radicals.

$\sqrt{6 \cdot 2} + \sqrt{6} (- 4 \sqrt{6}) + \sqrt{6} (3 \sqrt{15})$

Step 2.2

Multiply $\sqrt{6} (- 4 \sqrt{6})$ .

Tap for more steps...

Step 2.2.1

Raise $\sqrt{6}$ to the power of $1$ .

$\sqrt{6 \cdot 2} - 4 ({\sqrt{6}}^{1} \sqrt{6}) + \sqrt{6} (3 \sqrt{15})$

Step 2.2.2

Raise $\sqrt{6}$ to the power of $1$ .

$\sqrt{6 \cdot 2} - 4 ({\sqrt{6}}^{1} {\sqrt{6}}^{1}) + \sqrt{6} (3 \sqrt{15})$

Step 2.2.3

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

$\sqrt{6 \cdot 2} - 4 {\sqrt{6}}^{1 + 1} + \sqrt{6} (3 \sqrt{15})$

Step 2.2.4

Add $1$ and $1$ .

$\sqrt{6 \cdot 2} - 4 {\sqrt{6}}^{2} + \sqrt{6} (3 \sqrt{15})$

Step 2.3

Multiply $\sqrt{6} (3 \sqrt{15})$ .

Tap for more steps...

Step 2.3.1

Combine using the product rule for radicals.

$\sqrt{6 \cdot 2} - 4 {\sqrt{6}}^{2} + 3 \sqrt{6 \cdot 15}$

Step 2.3.2

Multiply $6$ by $15$ .

$\sqrt{6 \cdot 2} - 4 {\sqrt{6}}^{2} + 3 \sqrt{90}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $6$ by $2$ .

$\sqrt{12} - 4 {\sqrt{6}}^{2} + 3 \sqrt{90}$

Step 3.2

Rewrite $12$ as $2^{2} \cdot 3$ .

Tap for more steps...

Step 3.2.1

Factor $4$ out of $12$ .

$\sqrt{4 (3)} - 4 {\sqrt{6}}^{2} + 3 \sqrt{90}$

Step 3.2.2

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

$\sqrt{2^{2} \cdot 3} - 4 {\sqrt{6}}^{2} + 3 \sqrt{90}$

Step 3.3

Pull terms out from under the radical.

$2 \sqrt{3} - 4 {\sqrt{6}}^{2} + 3 \sqrt{90}$

Step 3.4

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Tap for more steps...

Step 3.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$2 \sqrt{3} - 4 {(6^{\frac{1}{2}})}^{2} + 3 \sqrt{90}$

Step 3.4.2

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

$2 \sqrt{3} - 4 \cdot 6^{\frac{1}{2} \cdot 2} + 3 \sqrt{90}$

Step 3.4.3

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

$2 \sqrt{3} - 4 \cdot 6^{\frac{2}{2}} + 3 \sqrt{90}$

Step 3.4.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.4.4.1

Cancel the common factor.

$2 \sqrt{3} - 4 \cdot 6^{\frac{2}{2}} + 3 \sqrt{90}$

Step 3.4.4.2

Rewrite the expression.

$2 \sqrt{3} - 4 \cdot 6^{1} + 3 \sqrt{90}$

Step 3.4.5

Evaluate the exponent.

$2 \sqrt{3} - 4 \cdot 6 + 3 \sqrt{90}$

Step 3.5

Multiply $- 4$ by $6$ .

$2 \sqrt{3} - 24 + 3 \sqrt{90}$

Step 3.6

Rewrite $90$ as $3^{2} \cdot 10$ .

Tap for more steps...

Step 3.6.1

Factor $9$ out of $90$ .

$2 \sqrt{3} - 24 + 3 \sqrt{9 (10)}$

Step 3.6.2

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

$2 \sqrt{3} - 24 + 3 \sqrt{3^{2} \cdot 10}$

Step 3.7

Pull terms out from under the radical.

$2 \sqrt{3} - 24 + 3 (3 \sqrt{10})$

Step 3.8

Multiply $3$ by $3$ .

$2 \sqrt{3} - 24 + 9 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3} - 24 + 9 \sqrt{10}$

Decimal Form:

$7.92460055 \dots$