Algebra Examples

$\sqrt{40 x^{4} y^{6}}$

Step 1

Rewrite $40 x^{4} y^{6}$ as ${(2 x^{2} y^{3})}^{2} \cdot 10$ .

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Step 1.1

Factor $4$ out of $40$ .

$\sqrt{4 (10) x^{4} y^{6}}$

Step 1.2

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

$\sqrt{2^{2} \cdot 10 x^{4} y^{6}}$

Step 1.3

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

$\sqrt{2^{2} \cdot 10 {(x^{2})}^{2} y^{6}}$

Step 1.4

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

$\sqrt{2^{2} \cdot 10 {(x^{2})}^{2} {(y^{3})}^{2}}$

Step 1.5

Move $10$ .

$\sqrt{2^{2} {(x^{2})}^{2} {(y^{3})}^{2} \cdot 10}$

Step 1.6

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

$\sqrt{{(2 x^{2} y^{3})}^{2} \cdot 10}$

Step 2

Pull terms out from under the radical.

$2 x^{2} y^{3} \sqrt{10}$