Pre-Algebra Examples

$\sqrt{6 (3 - \sqrt{6}) + 6 \sqrt{6}}$

Step 1

Apply the distributive property.

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

Step 2

Multiply $6$ by $3$ .

$\sqrt{18 + 6 (- \sqrt{6}) + 6 \sqrt{6}}$

Step 3

Multiply $- 1$ by $6$ .

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

Step 4

Add $- 6 \sqrt{6}$ and $6 \sqrt{6}$ .

$\sqrt{18 + 0}$

Step 5

Add $18$ and $0$ .

$\sqrt{18}$

Step 6

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 6.1

Factor $9$ out of $18$ .

$\sqrt{9 (2)}$

Step 6.2

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

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

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

Step 7

Pull terms out from under the radical.

$3 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

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