Algebra Examples

$3 \sqrt{5} (6 - 2 \sqrt{6})$

Step 1

Apply the distributive property.

$3 \sqrt{5} \cdot 6 + 3 \sqrt{5} (- 2 \sqrt{6})$

Step 2

Multiply $6$ by $3$ .

$18 \sqrt{5} + 3 \sqrt{5} (- 2 \sqrt{6})$

Step 3

Multiply $3 \sqrt{5} (- 2 \sqrt{6})$ .

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Step 3.1

Multiply $- 2$ by $3$ .

$18 \sqrt{5} - 6 \sqrt{5} \sqrt{6}$

Step 3.2

Combine using the product rule for radicals.

$18 \sqrt{5} - 6 \sqrt{6 \cdot 5}$

Step 3.3

Multiply $6$ by $5$ .

$18 \sqrt{5} - 6 \sqrt{30}$

$18 \sqrt{5} - 6 \sqrt{30}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$18 \sqrt{5} - 6 \sqrt{30}$

Decimal Form:

$7.38587014 \dots$

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