Algebra Examples

$- \sqrt{448 x^{6} y^{5}}$

Step 1

Rewrite $448 x^{6} y^{5}$ as ${(8 x^{3} y^{2})}^{2} \cdot (7 y)$ .

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Step 1.1

Factor $64$ out of $448$ .

$- \sqrt{64 (7) x^{6} y^{5}}$

Step 1.2

Rewrite $64$ as $8^{2}$ .

$- \sqrt{8^{2} \cdot 7 x^{6} y^{5}}$

Step 1.3

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$- \sqrt{8^{2} \cdot 7 {(x^{3})}^{2} y^{5}}$

Step 1.4

Factor out $y^{4}$ .

$- \sqrt{8^{2} \cdot 7 {(x^{3})}^{2} (y^{4} y)}$

Step 1.5

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

$- \sqrt{8^{2} \cdot 7 {(x^{3})}^{2} ({(y^{2})}^{2} y)}$

Step 1.6

Move $7$ .

$- \sqrt{8^{2} {(x^{3})}^{2} {(y^{2})}^{2} \cdot 7 y}$

Step 1.7

Rewrite $8^{2} {(x^{3})}^{2} {(y^{2})}^{2}$ as ${(8 x^{3} y^{2})}^{2}$ .

$- \sqrt{{(8 x^{3} y^{2})}^{2} \cdot 7 y}$

Step 1.8

Add parentheses.

$- \sqrt{{(8 x^{3} y^{2})}^{2} \cdot (7 y)}$

Step 2

Pull terms out from under the radical.

$- (| 8 x^{3} y^{2} | \sqrt{7 y})$

Step 3

Remove non-negative terms from the absolute value.

$- (8 y^{2} | x^{3} | \sqrt{7 y})$

Step 4

Multiply $8$ by $- 1$ .

$- 8 y^{2} | x^{3} | \sqrt{7 y}$