Basic Math Examples

$\frac{1}{2} \cdot \sqrt{80 a^{3}} - 4 a \sqrt{20 a}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $80 a^{3}$ as ${(4 a)}^{2} \cdot (5 a)$ .

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Step 1.1.1

Factor $16$ out of $80$ .

$\frac{1}{2} \cdot \sqrt{16 (5) a^{3}} - 4 a \sqrt{20 a}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{1}{2} \cdot \sqrt{4^{2} \cdot 5 a^{3}} - 4 a \sqrt{20 a}$

Step 1.1.3

Factor out $a^{2}$ .

$\frac{1}{2} \cdot \sqrt{4^{2} \cdot 5 (a^{2} a)} - 4 a \sqrt{20 a}$

Step 1.1.4

Move $5$ .

$\frac{1}{2} \cdot \sqrt{4^{2} a^{2} \cdot 5 a} - 4 a \sqrt{20 a}$

Step 1.1.5

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

$\frac{1}{2} \cdot \sqrt{{(4 a)}^{2} \cdot 5 a} - 4 a \sqrt{20 a}$

Step 1.1.6

Add parentheses.

$\frac{1}{2} \cdot \sqrt{{(4 a)}^{2} \cdot (5 a)} - 4 a \sqrt{20 a}$

Step 1.2

Pull terms out from under the radical.

$\frac{1}{2} \cdot (4 a \sqrt{5 a}) - 4 a \sqrt{20 a}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4 a \sqrt{5 a}$ .

$\frac{1}{2} \cdot (2 (2 a \sqrt{5 a})) - 4 a \sqrt{20 a}$

Step 1.3.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 (2 a \sqrt{5 a})) - 4 a \sqrt{20 a}$

Step 1.3.3

Rewrite the expression.

$2 a \sqrt{5 a} - 4 a \sqrt{20 a}$

Step 1.4

Rewrite $20 a$ as $2^{2} \cdot (5 a)$ .

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Step 1.4.1

Factor $4$ out of $20$ .

$2 a \sqrt{5 a} - 4 a \sqrt{4 (5) a}$

Step 1.4.2

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

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

Step 1.4.3

Add parentheses.

$2 a \sqrt{5 a} - 4 a \sqrt{2^{2} \cdot (5 a)}$

Step 1.5

Pull terms out from under the radical.

$2 a \sqrt{5 a} - 4 a (2 \sqrt{5 a})$

Step 1.6

Multiply $2$ by $- 4$ .

$2 a \sqrt{5 a} - 8 a \sqrt{5 a}$

Step 2

Subtract $8 a \sqrt{5 a}$ from $2 a \sqrt{5 a}$ .

$- 6 a \sqrt{5 a}$