Basic Math Examples

$3 \sqrt{50 a^{2}} - 3 \sqrt{72 a^{2}} - 8 a \sqrt{18}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $50 a^{2}$ as ${(5 a)}^{2} \cdot 2$ .

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Step 1.1.1

Factor $25$ out of $50$ .

$3 \sqrt{25 (2) a^{2}} - 3 \sqrt{72 a^{2}} - 8 a \sqrt{18}$

Step 1.1.2

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

$3 \sqrt{5^{2} \cdot 2 a^{2}} - 3 \sqrt{72 a^{2}} - 8 a \sqrt{18}$

Step 1.1.3

Move $2$ .

$3 \sqrt{5^{2} a^{2} \cdot 2} - 3 \sqrt{72 a^{2}} - 8 a \sqrt{18}$

Step 1.1.4

Rewrite $5^{2} a^{2}$ as ${(5 a)}^{2}$ .

$3 \sqrt{{(5 a)}^{2} \cdot 2} - 3 \sqrt{72 a^{2}} - 8 a \sqrt{18}$

Step 1.2

Pull terms out from under the radical.

$3 (5 a \sqrt{2}) - 3 \sqrt{72 a^{2}} - 8 a \sqrt{18}$

Step 1.3

Multiply $5$ by $3$ .

$15 (a \sqrt{2}) - 3 \sqrt{72 a^{2}} - 8 a \sqrt{18}$

Step 1.4

Rewrite $72 a^{2}$ as ${(6 a)}^{2} \cdot 2$ .

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Step 1.4.1

Factor $36$ out of $72$ .

$15 a \sqrt{2} - 3 \sqrt{36 (2) a^{2}} - 8 a \sqrt{18}$

Step 1.4.2

Rewrite $36$ as $6^{2}$ .

$15 a \sqrt{2} - 3 \sqrt{6^{2} \cdot 2 a^{2}} - 8 a \sqrt{18}$

Step 1.4.3

Move $2$ .

$15 a \sqrt{2} - 3 \sqrt{6^{2} a^{2} \cdot 2} - 8 a \sqrt{18}$

Step 1.4.4

Rewrite $6^{2} a^{2}$ as ${(6 a)}^{2}$ .

$15 a \sqrt{2} - 3 \sqrt{{(6 a)}^{2} \cdot 2} - 8 a \sqrt{18}$

Step 1.5

Pull terms out from under the radical.

$15 a \sqrt{2} - 3 (6 a \sqrt{2}) - 8 a \sqrt{18}$

Step 1.6

Multiply $6$ by $- 3$ .

$15 a \sqrt{2} - 18 (a \sqrt{2}) - 8 a \sqrt{18}$

Step 1.7

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

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Step 1.7.1

Factor $9$ out of $18$ .

$15 a \sqrt{2} - 18 a \sqrt{2} - 8 a \sqrt{9 (2)}$

Step 1.7.2

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

$15 a \sqrt{2} - 18 a \sqrt{2} - 8 a \sqrt{3^{2} \cdot 2}$

Step 1.8

Pull terms out from under the radical.

$15 a \sqrt{2} - 18 a \sqrt{2} - 8 a (3 \sqrt{2})$

Step 1.9

Multiply $3$ by $- 8$ .

$15 a \sqrt{2} - 18 a \sqrt{2} - 24 a \sqrt{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $18 a \sqrt{2}$ from $15 a \sqrt{2}$ .

$- 3 a \sqrt{2} - 24 a \sqrt{2}$

Step 2.2

Subtract $24 a \sqrt{2}$ from $- 3 a \sqrt{2}$ .

$- 27 a \sqrt{2}$