Precalculus Examples

$\sqrt{75} - \sqrt{3} + 2 \sqrt{27}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $25$ out of $75$ .

$\sqrt{25 (3)} - \sqrt{3} + 2 \sqrt{27}$

Step 1.1.2

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

$\sqrt{5^{2} \cdot 3} - \sqrt{3} + 2 \sqrt{27}$

$\sqrt{5^{2} \cdot 3} - \sqrt{3} + 2 \sqrt{27}$

Step 1.2

Pull terms out from under the radical.

$5 \sqrt{3} - \sqrt{3} + 2 \sqrt{27}$

Step 1.3

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

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Step 1.3.1

Factor $9$ out of $27$ .

$5 \sqrt{3} - \sqrt{3} + 2 \sqrt{9 (3)}$

Step 1.3.2

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

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $3$ by $2$ .

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

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $\sqrt{3}$ from $5 \sqrt{3}$ .

$4 \sqrt{3} + 6 \sqrt{3}$

Step 2.2

Add $4 \sqrt{3}$ and $6 \sqrt{3}$ .

$10 \sqrt{3}$

$10 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{3}$

Decimal Form:

$17.32050807 \dots$

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