Basic Math Examples

$\sqrt{3 a^{2} b} \cdot \sqrt{6 a b^{4}}$

Step 1

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

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Step 1.1

Reorder $3$ and $a^{2}$ .

$\sqrt{a^{2} \cdot 3 b} \cdot \sqrt{6 a b^{4}}$

Step 1.2

Add parentheses.

$\sqrt{a^{2} \cdot (3 b)} \cdot \sqrt{6 a b^{4}}$

Step 2

Pull terms out from under the radical.

$a \sqrt{3 b} \cdot \sqrt{6 a b^{4}}$

Step 3

Rewrite $6 a b^{4}$ as ${(b^{2})}^{2} \cdot (6 a)$ .

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Step 3.1

Rewrite $b^{4}$ as ${(b^{2})}^{2}$ .

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

Step 3.2

Move $a$ .

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

Step 3.3

Reorder $6$ and ${(b^{2})}^{2}$ .

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

Step 3.4

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $a \sqrt{3 b} (b^{2} \sqrt{6 a})$ .

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Step 5.1

Combine using the product rule for radicals.

$a (b^{2} \sqrt{3 b (6 a)})$

Step 5.2

Multiply $6$ by $3$ .

$a (b^{2} \sqrt{18 b a})$

Step 6

Rewrite $18 b a$ as $3^{2} \cdot (2 b a)$ .

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Step 6.1

Factor $9$ out of $18$ .

$a (b^{2} \sqrt{9 (2) b a})$

Step 6.2

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

$a (b^{2} \sqrt{3^{2} \cdot 2 b a})$

Step 6.3

Add parentheses.

$a (b^{2} \sqrt{3^{2} \cdot 2 (b a)})$

Step 6.4

Add parentheses.

$a (b^{2} \sqrt{3^{2} \cdot (2 b a)})$

Step 7

Pull terms out from under the radical.

$a (b^{2} (3 \sqrt{2 b a}))$

Step 8

Simplify the expression.

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Step 8.1

Rewrite using the commutative property of multiplication.

$3 a (b^{2} \sqrt{2 b a})$

Step 8.2

Reorder factors in $3 a (b^{2} \sqrt{2 b a})$ .

$3 a b^{2} \sqrt{2 b a}$