Algebra Examples

$\sqrt{5 x^{2} y} \sqrt{25 x y^{4}}$

Step 1

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

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Step 1.1

Reorder $5$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 5 y} \sqrt{25 x y^{4}}$

Step 1.2

Add parentheses.

$\sqrt{x^{2} \cdot (5 y)} \sqrt{25 x y^{4}}$

Step 2

Pull terms out from under the radical.

$x \sqrt{5 y} \sqrt{25 x y^{4}}$

Step 3

Rewrite $25 x y^{4}$ as ${(5 y^{2})}^{2} x$ .

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Move $x$ .

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

Step 3.4

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

Combine using the product rule for radicals.

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

Step 7

Reorder factors in $5 x (y^{2} \sqrt{5 y x})$ .

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