Basic Math Examples

$\sqrt{125 x^{6} y^{6}}$

Step 1

Rewrite $125 x^{6} y^{6}$ as ${(5 x^{3} y^{3})}^{2} \cdot 5$ .

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Step 1.1

Factor $25$ out of $125$ .

$\sqrt{25 (5) x^{6} y^{6}}$

Step 1.2

Rewrite $25$ as $5^{2}$ .

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

Step 1.3

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

$\sqrt{5^{2} \cdot 5 {(x^{3})}^{2} y^{6}}$

Step 1.4

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

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

Step 1.5

Move $5$ .

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

Step 1.6

Rewrite $5^{2} {(x^{3})}^{2} {(y^{3})}^{2}$ as ${(5 x^{3} y^{3})}^{2}$ .

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

Step 2

Pull terms out from under the radical.

$5 x^{3} y^{3} \sqrt{5}$