Basic Math Examples

$3 a^{3 \sqrt{200 a^{5}}} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 1

Rewrite $200 a^{5}$ as ${(10 a^{2})}^{2} \cdot (2 a)$ .

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Step 1.1

Factor $100$ out of $200$ .

$3 a^{3 \sqrt{100 (2) a^{5}}} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 1.2

Rewrite $100$ as $10^{2}$ .

$3 a^{3 \sqrt{10^{2} \cdot 2 a^{5}}} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 1.3

Factor out $a^{4}$ .

$3 a^{3 \sqrt{10^{2} \cdot 2 (a^{4} a)}} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 1.4

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

$3 a^{3 \sqrt{10^{2} \cdot 2 ({(a^{2})}^{2} a)}} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 1.5

Move $2$ .

$3 a^{3 \sqrt{10^{2} {(a^{2})}^{2} \cdot 2 a}} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 1.6

Rewrite $10^{2} {(a^{2})}^{2}$ as ${(10 a^{2})}^{2}$ .

$3 a^{3 \sqrt{{(10 a^{2})}^{2} \cdot 2 a}} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 1.7

Add parentheses.

$3 a^{3 \sqrt{{(10 a^{2})}^{2} \cdot (2 a)}} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 2

Pull terms out from under the radical.

$3 a^{3 (10 a^{2} \sqrt{2 a})} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 3

Multiply $10$ by $3$ .

$3 a^{30 (a^{2} \sqrt{2 a})} - 4 a^{4 \sqrt{72 a^{3}}}$

Step 4

Rewrite $72 a^{3}$ as ${(6 a)}^{2} \cdot (2 a)$ .

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Step 4.1

Factor $36$ out of $72$ .

$3 a^{30 a^{2} \sqrt{2 a}} - 4 a^{4 \sqrt{36 (2) a^{3}}}$

Step 4.2

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

$3 a^{30 a^{2} \sqrt{2 a}} - 4 a^{4 \sqrt{6^{2} \cdot 2 a^{3}}}$

Step 4.3

Factor out $a^{2}$ .

$3 a^{30 a^{2} \sqrt{2 a}} - 4 a^{4 \sqrt{6^{2} \cdot 2 (a^{2} a)}}$

Step 4.4

Move $2$ .

$3 a^{30 a^{2} \sqrt{2 a}} - 4 a^{4 \sqrt{6^{2} a^{2} \cdot 2 a}}$

Step 4.5

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

$3 a^{30 a^{2} \sqrt{2 a}} - 4 a^{4 \sqrt{{(6 a)}^{2} \cdot 2 a}}$

Step 4.6

Add parentheses.

$3 a^{30 a^{2} \sqrt{2 a}} - 4 a^{4 \sqrt{{(6 a)}^{2} \cdot (2 a)}}$

Step 5

Pull terms out from under the radical.

$3 a^{30 a^{2} \sqrt{2 a}} - 4 a^{4 (6 a \sqrt{2 a})}$

Step 6

Multiply $6$ by $4$ .

$3 a^{30 a^{2} \sqrt{2 a}} - 4 a^{24 a \sqrt{2 a}}$