Finite Math Examples

$- 3 \sqrt{81} - 4 \sqrt{243} + 5 \sqrt{135}$

Step 1

Rewrite $81$ as $9^{2}$ .

$- 3 \sqrt{9^{2}} - 4 \sqrt{243} + 5 \sqrt{135}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$- 3 \cdot 9 - 4 \sqrt{243} + 5 \sqrt{135}$

Step 3

Multiply $- 3$ by $9$ .

$- 27 - 4 \sqrt{243} + 5 \sqrt{135}$

Step 4

Rewrite $243$ as $9^{2} \cdot 3$ .

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Step 4.1

Factor $81$ out of $243$ .

$- 27 - 4 \sqrt{81 (3)} + 5 \sqrt{135}$

Step 4.2

Rewrite $81$ as $9^{2}$ .

$- 27 - 4 \sqrt{9^{2} \cdot 3} + 5 \sqrt{135}$

$- 27 - 4 \sqrt{9^{2} \cdot 3} + 5 \sqrt{135}$

Step 5

Pull terms out from under the radical.

$- 27 - 4 (9 \sqrt{3}) + 5 \sqrt{135}$

Step 6

Multiply $9$ by $- 4$ .

$- 27 - 36 \sqrt{3} + 5 \sqrt{135}$

Step 7

Rewrite $135$ as $3^{2} \cdot 15$ .

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Step 7.1

Factor $9$ out of $135$ .

$- 27 - 36 \sqrt{3} + 5 \sqrt{9 (15)}$

Step 7.2

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

$- 27 - 36 \sqrt{3} + 5 \sqrt{3^{2} \cdot 15}$

$- 27 - 36 \sqrt{3} + 5 \sqrt{3^{2} \cdot 15}$

Step 8

Pull terms out from under the radical.

$- 27 - 36 \sqrt{3} + 5 (3 \sqrt{15})$

Step 9

Multiply $3$ by $5$ .

$- 27 - 36 \sqrt{3} + 15 \sqrt{15}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- 27 - 36 \sqrt{3} + 15 \sqrt{15}$

Decimal Form:

$- 31.25907887 \dots$

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