Finite Math Examples

$w \sqrt{80 y^{5}} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 1

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

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Step 1.1

Factor $16$ out of $80$ .

$w \sqrt{16 (5) y^{5}} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 1.2

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

$w \sqrt{4^{2} \cdot 5 y^{5}} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 1.3

Factor out $y^{4}$ .

$w \sqrt{4^{2} \cdot 5 (y^{4} y)} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 1.4

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

$w \sqrt{4^{2} \cdot 5 ({(y^{2})}^{2} y)} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 1.5

Move $5$ .

$w \sqrt{4^{2} {(y^{2})}^{2} \cdot 5 y} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 1.6

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

$w \sqrt{{(4 y^{2})}^{2} \cdot 5 y} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 1.7

Add parentheses.

$w \sqrt{{(4 y^{2})}^{2} \cdot (5 y)} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 2

Pull terms out from under the radical.

$w (4 y^{2} \sqrt{5 y}) - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 3

Rewrite using the commutative property of multiplication.

$4 w y^{2} \sqrt{5 y} - 8 y^{2 \sqrt{45 y w^{2}}}$

Step 4

Rewrite $45 y w^{2}$ as ${(3 w)}^{2} \cdot (5 y)$ .

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Step 4.1

Factor $9$ out of $45$ .

$4 w y^{2} \sqrt{5 y} - 8 y^{2 \sqrt{9 (5) y w^{2}}}$

Step 4.2

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

$4 w y^{2} \sqrt{5 y} - 8 y^{2 \sqrt{3^{2} \cdot 5 y w^{2}}}$

Step 4.3

Move $y$ .

$4 w y^{2} \sqrt{5 y} - 8 y^{2 \sqrt{3^{2} \cdot 5 w^{2} y}}$

Step 4.4

Move $5$ .

$4 w y^{2} \sqrt{5 y} - 8 y^{2 \sqrt{3^{2} w^{2} \cdot 5 y}}$

Step 4.5

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

$4 w y^{2} \sqrt{5 y} - 8 y^{2 \sqrt{{(3 w)}^{2} \cdot 5 y}}$

Step 4.6

Add parentheses.

$4 w y^{2} \sqrt{5 y} - 8 y^{2 \sqrt{{(3 w)}^{2} \cdot (5 y)}}$

Step 5

Pull terms out from under the radical.

$4 w y^{2} \sqrt{5 y} - 8 y^{2 (3 w \sqrt{5 y})}$

Step 6

Multiply $3$ by $2$ .

$4 w y^{2} \sqrt{5 y} - 8 y^{6 w \sqrt{5 y}}$