Basic Math Examples

$a^{2 \sqrt[4]{4 a^{2}} + \sqrt{18 a^{5}} - a \sqrt{2 a^{3}}}$

Step 1

Simplify each term.

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Step 1.1

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

$a^{2 \sqrt[4]{{(2 a)}^{2}} + \sqrt{18 a^{5}} - a \sqrt{2 a^{3}}}$

Step 1.2

Rewrite $\sqrt[4]{{(2 a)}^{2}}$ as $\sqrt{\sqrt{{(2 a)}^{2}}}$ .

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

Step 1.3

Pull terms out from under the radical, assuming positive real numbers.

$a^{2 \sqrt{2 a} + \sqrt{18 a^{5}} - a \sqrt{2 a^{3}}}$

Step 1.4

Rewrite $18 a^{5}$ as ${(3 a^{2})}^{2} \cdot (2 a)$ .

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Step 1.4.1

Factor $9$ out of $18$ .

$a^{2 \sqrt{2 a} + \sqrt{9 (2) a^{5}} - a \sqrt{2 a^{3}}}$

Step 1.4.2

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

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

Step 1.4.3

Factor out $a^{4}$ .

$a^{2 \sqrt{2 a} + \sqrt{3^{2} \cdot 2 (a^{4} a)} - a \sqrt{2 a^{3}}}$

Step 1.4.4

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

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

Step 1.4.5

Move $2$ .

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

Step 1.4.6

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

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

Step 1.4.7

Add parentheses.

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

Step 1.5

Pull terms out from under the radical.

$a^{2 \sqrt{2 a} + 3 a^{2} \sqrt{2 a} - a \sqrt{2 a^{3}}}$

Step 1.6

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

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Step 1.6.1

Factor out $a^{2}$ .

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

Step 1.6.2

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

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

Step 1.6.3

Add parentheses.

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

Step 1.7

Pull terms out from under the radical.

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

Step 1.8

Multiply $a$ by $a$ by adding the exponents.

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Step 1.8.1

Move $a$ .

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

Step 1.8.2

Multiply $a$ by $a$ .

$a^{2 \sqrt{2 a} + 3 a^{2} \sqrt{2 a} - a^{2} \sqrt{2 a}}$

Step 2

Subtract $a^{2} \sqrt{2 a}$ from $3 a^{2} \sqrt{2 a}$ .

$a^{2 \sqrt{2 a} + 2 a^{2} \sqrt{2 a}}$