Algebra Examples

$2 \sqrt{45} + 2 \sqrt{90} + 3 \sqrt{45}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 1.1.1

Factor $9$ out of $45$ .

$2 \sqrt{9 (5)} + 2 \sqrt{90} + 3 \sqrt{45}$

Step 1.1.2

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

$2 \sqrt{3^{2} \cdot 5} + 2 \sqrt{90} + 3 \sqrt{45}$

Step 1.2

Pull terms out from under the radical.

$2 (| 3 | \sqrt{5}) + 2 \sqrt{90} + 3 \sqrt{45}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$2 (3 \sqrt{5}) + 2 \sqrt{90} + 3 \sqrt{45}$

Step 1.4

Multiply $3$ by $2$ .

$6 \sqrt{5} + 2 \sqrt{90} + 3 \sqrt{45}$

Step 1.5

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 1.5.1

Factor $9$ out of $90$ .

$6 \sqrt{5} + 2 \sqrt{9 (10)} + 3 \sqrt{45}$

Step 1.5.2

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

$6 \sqrt{5} + 2 \sqrt{3^{2} \cdot 10} + 3 \sqrt{45}$

Step 1.6

Pull terms out from under the radical.

$6 \sqrt{5} + 2 (| 3 | \sqrt{10}) + 3 \sqrt{45}$

Step 1.7

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$6 \sqrt{5} + 2 (3 \sqrt{10}) + 3 \sqrt{45}$

Step 1.8

Multiply $3$ by $2$ .

$6 \sqrt{5} + 6 \sqrt{10} + 3 \sqrt{45}$

Step 1.9

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 1.9.1

Factor $9$ out of $45$ .

$6 \sqrt{5} + 6 \sqrt{10} + 3 \sqrt{9 (5)}$

Step 1.9.2

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

$6 \sqrt{5} + 6 \sqrt{10} + 3 \sqrt{3^{2} \cdot 5}$

Step 1.10

Pull terms out from under the radical.

$6 \sqrt{5} + 6 \sqrt{10} + 3 (| 3 | \sqrt{5})$

Step 1.11

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$6 \sqrt{5} + 6 \sqrt{10} + 3 (3 \sqrt{5})$

Step 1.12

Multiply $3$ by $3$ .

$6 \sqrt{5} + 6 \sqrt{10} + 9 \sqrt{5}$

Step 2

Add $6 \sqrt{5}$ and $9 \sqrt{5}$ .

$15 \sqrt{5} + 6 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{5} + 6 \sqrt{10}$

Decimal Form:

$52.51468562 \dots$