Algebra Examples

$\sqrt{15 x y^{2}} \cdot \sqrt{5 x^{2} y}$

Step 1

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

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Step 1.1

Move $x$ .

$\sqrt{15 y^{2} x} \cdot \sqrt{5 x^{2} y}$

Step 1.2

Reorder $15$ and $y^{2}$ .

$\sqrt{y^{2} \cdot 15 x} \cdot \sqrt{5 x^{2} y}$

Step 1.3

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

$y \sqrt{15 x} \cdot \sqrt{5 x^{2} y}$

Step 3

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

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Step 3.1

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

$y \sqrt{15 x} \cdot \sqrt{x^{2} \cdot 5 y}$

Step 3.2

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

$y \sqrt{15 x} \cdot (x \sqrt{5 y})$

Step 5

Multiply $y \sqrt{15 x} (x \sqrt{5 y})$ .

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Step 5.1

Combine using the product rule for radicals.

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

Step 5.2

Multiply $5$ by $15$ .

$y (x \sqrt{75 x y})$

$y (x \sqrt{75 x y})$

Step 6

Rewrite $75 x y$ as $5^{2} \cdot (3 x y)$ .

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Step 6.1

Factor $25$ out of $75$ .

$y (x \sqrt{25 (3) x y})$

Step 6.2

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

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

Step 6.3

Add parentheses.

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

Step 6.4

Add parentheses.

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

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

Step 7

Pull terms out from under the radical.

$y (x (5 \sqrt{3 x y}))$

Step 8

Simplify the expression.

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Step 8.1

Rewrite using the commutative property of multiplication.

$5 y (x \sqrt{3 x y})$

Step 8.2

Reorder factors in $5 y (x \sqrt{3 x y})$ .

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$