Basic Math Examples

$- 5 \sqrt{45} + 6 \sqrt{20} + 3 \sqrt{5}$

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 $45$ .

$- 5 \sqrt{9 (5)} + 6 \sqrt{20} + 3 \sqrt{5}$

Step 1.1.2

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

$- 5 \sqrt{3^{2} \cdot 5} + 6 \sqrt{20} + 3 \sqrt{5}$

Step 1.2

Pull terms out from under the radical.

$- 5 (3 \sqrt{5}) + 6 \sqrt{20} + 3 \sqrt{5}$

Step 1.3

Multiply $3$ by $- 5$ .

$- 15 \sqrt{5} + 6 \sqrt{20} + 3 \sqrt{5}$

Step 1.4

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.4.1

Factor $4$ out of $20$ .

$- 15 \sqrt{5} + 6 \sqrt{4 (5)} + 3 \sqrt{5}$

Step 1.4.2

Rewrite $4$ as $2^{2}$ .

$- 15 \sqrt{5} + 6 \sqrt{2^{2} \cdot 5} + 3 \sqrt{5}$

Step 1.5

Pull terms out from under the radical.

$- 15 \sqrt{5} + 6 (2 \sqrt{5}) + 3 \sqrt{5}$

Step 1.6

Multiply $2$ by $6$ .

$- 15 \sqrt{5} + 12 \sqrt{5} + 3 \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 15 \sqrt{5}$ and $12 \sqrt{5}$ .

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

Step 2.2

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

$0$