Basic Math Examples

$\sqrt{225 x^{3} y^{11}}$

Step 1

Rewrite $225 x^{3} y^{11}$ as ${(15 x y^{5})}^{2} (x y)$ .

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Step 1.1

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2} x^{3} y^{11}}$

Step 1.2

Factor out $x^{2}$ .

$\sqrt{15^{2} (x^{2} x) y^{11}}$

Step 1.3

Factor out $y^{10}$ .

$\sqrt{15^{2} (x^{2} x) (y^{10} y)}$

Step 1.4

Rewrite $y^{10}$ as ${(y^{5})}^{2}$ .

$\sqrt{15^{2} (x^{2} x) ({(y^{5})}^{2} y)}$

Step 1.5

Move $x$ .

$\sqrt{15^{2} (x^{2}) {(y^{5})}^{2} x y}$

Step 1.6

Rewrite $15^{2} (x^{2}) {(y^{5})}^{2}$ as ${(15 x y^{5})}^{2}$ .

$\sqrt{{(15 x y^{5})}^{2} x y}$

Step 1.7

Add parentheses.

$\sqrt{{(15 x y^{5})}^{2} (x y)}$

Step 2

Pull terms out from under the radical.

$15 x y^{5} \sqrt{x y}$