Algebra Examples

$\sqrt{5 x^{8} y^{2}} \cdot \sqrt{10 x y^{3}}$

Step 1

Rewrite $5 x^{8} y^{2}$ as ${(x^{4} y)}^{2} \cdot 5$ .

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Step 1.1

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{5 {(x^{4})}^{2} y^{2}} \cdot \sqrt{10 x y^{3}}$

Step 1.2

Move $5$ .

$\sqrt{{(x^{4})}^{2} y^{2} \cdot 5} \cdot \sqrt{10 x y^{3}}$

Step 1.3

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

$\sqrt{{(x^{4} y)}^{2} \cdot 5} \cdot \sqrt{10 x y^{3}}$

Step 2

Pull terms out from under the radical.

$x^{4} y \sqrt{5} \cdot \sqrt{10 x y^{3}}$

Step 3

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

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Step 3.1

Factor out $y^{2}$ .

$x^{4} y \sqrt{5} \cdot \sqrt{10 x (y^{2} y)}$

Step 3.2

Move $x$ .

$x^{4} y \sqrt{5} \cdot \sqrt{10 y^{2} x y}$

Step 3.3

Reorder $10$ and $y^{2}$ .

$x^{4} y \sqrt{5} \cdot \sqrt{y^{2} \cdot 10 x y}$

Step 3.4

Add parentheses.

$x^{4} y \sqrt{5} \cdot \sqrt{y^{2} \cdot 10 (x y)}$

Step 3.5

Add parentheses.

$x^{4} y \sqrt{5} \cdot \sqrt{y^{2} \cdot (10 x y)}$

Step 4

Pull terms out from under the radical.

$x^{4} y \sqrt{5} \cdot (y \sqrt{10 x y})$

Step 5

Multiply $y$ by $y$ by adding the exponents.

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Step 5.1

Move $y$ .

$x^{4} (y \cdot y) \sqrt{5} \cdot \sqrt{10 x y}$

Step 5.2

Multiply $y$ by $y$ .

$x^{4} y^{2} \sqrt{5} \cdot \sqrt{10 x y}$

Step 6

Multiply $x^{4} y^{2} \sqrt{5} \sqrt{10 x y}$ .

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Step 6.1

Combine using the product rule for radicals.

$x^{4} y^{2} \sqrt{10 x y \cdot 5}$

Step 6.2

Multiply $5$ by $10$ .

$x^{4} y^{2} \sqrt{50 x y}$

Step 7

Rewrite $50 x y$ as $5^{2} \cdot (2 x y)$ .

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Step 7.1

Factor $25$ out of $50$ .

$x^{4} y^{2} \sqrt{25 (2) x y}$

Step 7.2

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

$x^{4} y^{2} \sqrt{5^{2} \cdot 2 x y}$

Step 7.3

Add parentheses.

$x^{4} y^{2} \sqrt{5^{2} \cdot 2 (x y)}$

Step 7.4

Add parentheses.

$x^{4} y^{2} \sqrt{5^{2} \cdot (2 x y)}$

Step 8

Pull terms out from under the radical.

$x^{4} y^{2} (5 \sqrt{2 x y})$

Step 9

Rewrite using the commutative property of multiplication.

$5 x^{4} y^{2} \sqrt{2 x y}$