Algebra Examples

$6 \sqrt{27} - 2 \sqrt{18} + \sqrt{75}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $27$ .

$6 \sqrt{9 (3)} - 2 \sqrt{18} + \sqrt{75}$

Step 1.1.2

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

$6 \sqrt{3^{2} \cdot 3} - 2 \sqrt{18} + \sqrt{75}$

$6 \sqrt{3^{2} \cdot 3} - 2 \sqrt{18} + \sqrt{75}$

Step 1.2

Pull terms out from under the radical.

$6 (3 \sqrt{3}) - 2 \sqrt{18} + \sqrt{75}$

Step 1.3

Multiply $3$ by $6$ .

$18 \sqrt{3} - 2 \sqrt{18} + \sqrt{75}$

Step 1.4

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

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Step 1.4.1

Factor $9$ out of $18$ .

$18 \sqrt{3} - 2 \sqrt{9 (2)} + \sqrt{75}$

Step 1.4.2

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

$18 \sqrt{3} - 2 \sqrt{3^{2} \cdot 2} + \sqrt{75}$

$18 \sqrt{3} - 2 \sqrt{3^{2} \cdot 2} + \sqrt{75}$

Step 1.5

Pull terms out from under the radical.

$18 \sqrt{3} - 2 (3 \sqrt{2}) + \sqrt{75}$

Step 1.6

Multiply $3$ by $- 2$ .

$18 \sqrt{3} - 6 \sqrt{2} + \sqrt{75}$

Step 1.7

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.7.1

Factor $25$ out of $75$ .

$18 \sqrt{3} - 6 \sqrt{2} + \sqrt{25 (3)}$

Step 1.7.2

Rewrite $25$ as $5^{2}$ .

$18 \sqrt{3} - 6 \sqrt{2} + \sqrt{5^{2} \cdot 3}$

$18 \sqrt{3} - 6 \sqrt{2} + \sqrt{5^{2} \cdot 3}$

Step 1.8

Pull terms out from under the radical.

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

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

Step 2

Add $18 \sqrt{3}$ and $5 \sqrt{3}$ .

$23 \sqrt{3} - 6 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$23 \sqrt{3} - 6 \sqrt{2}$

Decimal Form:

$31.35188719 \dots$

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