Simplify 7 square root of 3y^2*2 square root of 6x^3y

$7 \sqrt{3 y^{2}} \cdot 2 \sqrt{6 x^{3} y}$

Step 1

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

$7 \sqrt{y^{2} \cdot 3} \cdot (2 \sqrt{6 x^{3} y})$

Step 2

Pull terms out from under the radical.

$7 (y \sqrt{3}) \cdot (2 \sqrt{6 x^{3} y})$

Step 3

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

Factor out $x^{2}$ .

$7 y \sqrt{3} \cdot (2 \sqrt{6 (x^{2} x) y})$

Reorder $6$ and $x^{2}$ .

$7 y \sqrt{3} \cdot (2 \sqrt{x^{2} \cdot 6 x y})$

Add parentheses.

$7 y \sqrt{3} \cdot (2 \sqrt{x^{2} \cdot 6 (x y)})$

Add parentheses.

$7 y \sqrt{3} \cdot (2 \sqrt{x^{2} \cdot (6 x y)})$

Step 4

Pull terms out from under the radical.

$7 y \sqrt{3} \cdot (2 (x \sqrt{6 x y}))$

Step 5

Multiply $7 y \sqrt{3} (2 x \sqrt{6 x y})$ .

Multiply $2$ by $7$ .

$14 y \sqrt{3} (x \sqrt{6 x y})$

Combine using the product rule for radicals.

$14 y (x \sqrt{3 (6 x y)})$

Multiply $3$ by $6$ .

$14 y (x \sqrt{18 x y})$

Step 6

Rewrite $18 x y$ as $3^{2} \cdot (2 x y)$ .

Factor $9$ out of $18$ .

$14 y (x \sqrt{9 (2) x y})$

Rewrite $9$ as $3^{2}$ .

$14 y (x \sqrt{3^{2} \cdot 2 x y})$

Add parentheses.

$14 y (x \sqrt{3^{2} \cdot 2 (x y)})$

Add parentheses.

$14 y (x \sqrt{3^{2} \cdot (2 x y)})$

Step 7

Pull terms out from under the radical.

$14 y (x (3 \sqrt{2 x y}))$

Step 8

Simplify the expression.

Rewrite using the commutative property of multiplication.

$14 y (3 x \sqrt{2 x y})$

Multiply $3$ by $14$ .

$42 y (x \sqrt{2 x y})$

Reorder factors in $42 y (x \sqrt{2 x y})$ .

$42 y x \sqrt{2 x y}$

Simplify 7 square root of 3y^2*2 square root of 6x^3y

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