Trigonometry Examples

$\sqrt[3]{6 a^{4} b^{2}} + \sqrt[3]{162 a^{4} b^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $6 a^{4} b^{2}$ as $a^{3} \cdot (6 a b^{2})$ .

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Step 1.1.1

Factor out $a^{3}$ .

$\sqrt[3]{6 (a^{3} a) b^{2}} + \sqrt[3]{162 a^{4} b^{2}}$

Step 1.1.2

Reorder $6$ and $a^{3}$ .

$\sqrt[3]{a^{3} \cdot 6 a b^{2}} + \sqrt[3]{162 a^{4} b^{2}}$

Step 1.1.3

Add parentheses.

$\sqrt[3]{a^{3} \cdot 6 (a b^{2})} + \sqrt[3]{162 a^{4} b^{2}}$

Step 1.1.4

Add parentheses.

$\sqrt[3]{a^{3} \cdot (6 a b^{2})} + \sqrt[3]{162 a^{4} b^{2}}$

Step 1.2

Pull terms out from under the radical.

$a \sqrt[3]{6 a b^{2}} + \sqrt[3]{162 a^{4} b^{2}}$

Step 1.3

Rewrite $162 a^{4} b^{2}$ as ${(3 a)}^{3} \cdot (6 a b^{2})$ .

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Step 1.3.1

Factor $27$ out of $162$ .

$a \sqrt[3]{6 a b^{2}} + \sqrt[3]{27 (6) a^{4} b^{2}}$

Step 1.3.2

Rewrite $27$ as $3^{3}$ .

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

Step 1.3.3

Factor out $a^{3}$ .

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

Step 1.3.4

Move $6$ .

$a \sqrt[3]{6 a b^{2}} + \sqrt[3]{3^{3} a^{3} \cdot 6 a b^{2}}$

Step 1.3.5

Rewrite $3^{3} a^{3}$ as ${(3 a)}^{3}$ .

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

Step 1.3.6

Add parentheses.

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

Step 1.3.7

Add parentheses.

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

Step 1.4

Pull terms out from under the radical.

$a \sqrt[3]{6 a b^{2}} + 3 a \sqrt[3]{6 a b^{2}}$

Step 2

Add $a \sqrt[3]{6 a b^{2}}$ and $3 a \sqrt[3]{6 a b^{2}}$ .

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