Simplify square root of 3x* square root of 2x*4 square root of 3x^2

$\sqrt{3 x} \cdot \sqrt{2 x} \cdot 4 \sqrt{3 x^{2}}$

Step 1

Rewrite using the commutative property of multiplication.

$4 \sqrt{3 x} \sqrt{2 x} \sqrt{3 x^{2}}$

Step 2

Multiply $4 \sqrt{3 x} \sqrt{2 x}$ .

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

$4 \sqrt{6 x \cdot x} \sqrt{3 x^{2}}$

Raise $x$ to the power of $1$ .

$4 \sqrt{6 (x^{1} x)} \sqrt{3 x^{2}}$

Raise $x$ to the power of $1$ .

$4 \sqrt{6 (x^{1} x^{1})} \sqrt{3 x^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \sqrt{6 x^{1 + 1}} \sqrt{3 x^{2}}$

Add $1$ and $1$ .

$4 \sqrt{6 x^{2}} \sqrt{3 x^{2}}$

Step 3

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

$4 \sqrt{x^{2} \cdot 6} \sqrt{3 x^{2}}$

Step 4

Pull terms out from under the radical.

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

Step 5

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

$4 x \sqrt{6} \sqrt{x^{2} \cdot 3}$

Step 6

Pull terms out from under the radical.

$4 x \sqrt{6} (x \sqrt{3})$

Step 7

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$4 (x \cdot x) \sqrt{6} \sqrt{3}$

Multiply $x$ by $x$ .

$4 x^{2} \sqrt{6} \sqrt{3}$

Step 8

Multiply $4 x^{2} \sqrt{6} \sqrt{3}$ .

Combine using the product rule for radicals.

$4 x^{2} \sqrt{3 \cdot 6}$

Multiply $3$ by $6$ .

$4 x^{2} \sqrt{18}$

Step 9

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$4 x^{2} \sqrt{9 (2)}$

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

$4 x^{2} \sqrt{3^{2} \cdot 2}$

Step 10

Pull terms out from under the radical.

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

Step 11

Multiply $3$ by $4$ .

$12 x^{2} \sqrt{2}$

Simplify square root of 3x* square root of 2x*4 square root of 3x^2

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