Finite Math Examples

$6 x \sqrt{3 y^{5}} + y^{2} \sqrt{12 y x^{2}}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor out $y^{4}$ .

$6 x \sqrt{3 (y^{4} y)} + y^{2} \sqrt{12 y x^{2}}$

Step 1.1.2

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

$6 x \sqrt{3 ({(y^{2})}^{2} y)} + y^{2} \sqrt{12 y x^{2}}$

Step 1.1.3

Reorder $3$ and ${(y^{2})}^{2}$ .

$6 x \sqrt{{(y^{2})}^{2} \cdot 3 y} + y^{2} \sqrt{12 y x^{2}}$

Step 1.1.4

Add parentheses.

$6 x \sqrt{{(y^{2})}^{2} \cdot (3 y)} + y^{2} \sqrt{12 y x^{2}}$

Step 1.2

Pull terms out from under the radical.

$6 x (y^{2} \sqrt{3 y}) + y^{2} \sqrt{12 y x^{2}}$

Step 1.3

Rewrite $12 y x^{2}$ as ${(2 x)}^{2} \cdot (3 y)$ .

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Step 1.3.1

Factor $4$ out of $12$ .

$6 x y^{2} \sqrt{3 y} + y^{2} \sqrt{4 (3) y x^{2}}$

Step 1.3.2

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

$6 x y^{2} \sqrt{3 y} + y^{2} \sqrt{2^{2} \cdot 3 y x^{2}}$

Step 1.3.3

Move $y$ .

$6 x y^{2} \sqrt{3 y} + y^{2} \sqrt{2^{2} \cdot 3 x^{2} y}$

Step 1.3.4

Move $3$ .

$6 x y^{2} \sqrt{3 y} + y^{2} \sqrt{2^{2} x^{2} \cdot 3 y}$

Step 1.3.5

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

$6 x y^{2} \sqrt{3 y} + y^{2} \sqrt{{(2 x)}^{2} \cdot 3 y}$

Step 1.3.6

Add parentheses.

$6 x y^{2} \sqrt{3 y} + y^{2} \sqrt{{(2 x)}^{2} \cdot (3 y)}$

Step 1.4

Pull terms out from under the radical.

$6 x y^{2} \sqrt{3 y} + y^{2} (2 x \sqrt{3 y})$

Step 1.5

Rewrite using the commutative property of multiplication.

$6 x y^{2} \sqrt{3 y} + 2 y^{2} (x \sqrt{3 y})$

Step 2

Add $6 x y^{2} \sqrt{3 y}$ and $2 y^{2} (x \sqrt{3 y})$ .

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Step 2.1

Move $y^{2}$ .

$6 x y^{2} \sqrt{3 y} + 2 x y^{2} \sqrt{3 y}$

Step 2.2

Add $6 x y^{2} \sqrt{3 y}$ and $2 x y^{2} \sqrt{3 y}$ .

$8 x y^{2} \sqrt{3 y}$