Algebra Examples

$3 \sqrt{12 a b^{2}} + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $12 a b^{2}$ as ${(2 b)}^{2} \cdot (3 a)$ .

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Step 1.1.1

Factor $4$ out of $12$ .

$3 \sqrt{4 (3) a b^{2}} + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1.1.2

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

$3 \sqrt{2^{2} \cdot 3 a b^{2}} + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1.1.3

Move $a$ .

$3 \sqrt{2^{2} \cdot 3 b^{2} a} + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1.1.4

Move $3$ .

$3 \sqrt{2^{2} b^{2} \cdot 3 a} + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1.1.5

Rewrite $2^{2} b^{2}$ as ${(2 b)}^{2}$ .

$3 \sqrt{{(2 b)}^{2} \cdot 3 a} + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1.1.6

Add parentheses.

$3 \sqrt{{(2 b)}^{2} \cdot (3 a)} + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1.2

Pull terms out from under the radical.

$3 (2 b \sqrt{3 a}) + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1.3

Multiply $2$ by $3$ .

$6 (b \sqrt{3 a}) + 3 b \sqrt{75 a} - 3 \sqrt{27 a b^{2}}$

Step 1.4

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

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Step 1.4.1

Factor $25$ out of $75$ .

$6 b \sqrt{3 a} + 3 b \sqrt{25 (3) a} - 3 \sqrt{27 a b^{2}}$

Step 1.4.2

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

$6 b \sqrt{3 a} + 3 b \sqrt{5^{2} \cdot 3 a} - 3 \sqrt{27 a b^{2}}$

Step 1.4.3

Add parentheses.

$6 b \sqrt{3 a} + 3 b \sqrt{5^{2} \cdot (3 a)} - 3 \sqrt{27 a b^{2}}$

Step 1.5

Pull terms out from under the radical.

$6 b \sqrt{3 a} + 3 b (5 \sqrt{3 a}) - 3 \sqrt{27 a b^{2}}$

Step 1.6

Multiply $5$ by $3$ .

$6 b \sqrt{3 a} + 15 b \sqrt{3 a} - 3 \sqrt{27 a b^{2}}$

Step 1.7

Rewrite $27 a b^{2}$ as ${(3 b)}^{2} \cdot (3 a)$ .

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Step 1.7.1

Factor $9$ out of $27$ .

$6 b \sqrt{3 a} + 15 b \sqrt{3 a} - 3 \sqrt{9 (3) a b^{2}}$

Step 1.7.2

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

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

Step 1.7.3

Move $a$ .

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

Step 1.7.4

Move $3$ .

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

Step 1.7.5

Rewrite $3^{2} b^{2}$ as ${(3 b)}^{2}$ .

$6 b \sqrt{3 a} + 15 b \sqrt{3 a} - 3 \sqrt{{(3 b)}^{2} \cdot 3 a}$

Step 1.7.6

Add parentheses.

$6 b \sqrt{3 a} + 15 b \sqrt{3 a} - 3 \sqrt{{(3 b)}^{2} \cdot (3 a)}$

Step 1.8

Pull terms out from under the radical.

$6 b \sqrt{3 a} + 15 b \sqrt{3 a} - 3 (3 b \sqrt{3 a})$

Step 1.9

Multiply $3$ by $- 3$ .

$6 b \sqrt{3 a} + 15 b \sqrt{3 a} - 9 b \sqrt{3 a}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $6 b \sqrt{3 a}$ and $15 b \sqrt{3 a}$ .

$21 b \sqrt{3 a} - 9 b \sqrt{3 a}$

Step 2.2

Subtract $9 b \sqrt{3 a}$ from $21 b \sqrt{3 a}$ .

$12 b \sqrt{3 a}$