Simplify square root of 6a^2b^4c* square root of 3a^6b^2c

$\sqrt{6 a^{2} b^{4} c} \cdot \sqrt{3 a^{6} b^{2} c}$

Rewrite $6 a^{2} b^{4} c$ as ${(a b^{2})}^{2} \cdot (6 c)$ .

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

$\sqrt{6 a^{2} {(b^{2})}^{2} c} \cdot \sqrt{3 a^{6} b^{2} c}$

Move $6$ .

$\sqrt{a^{2} {(b^{2})}^{2} \cdot 6 c} \cdot \sqrt{3 a^{6} b^{2} c}$

Rewrite $a^{2} {(b^{2})}^{2}$ as ${(a b^{2})}^{2}$ .

$\sqrt{{(a b^{2})}^{2} \cdot 6 c} \cdot \sqrt{3 a^{6} b^{2} c}$

Add parentheses.

$\sqrt{{(a b^{2})}^{2} \cdot (6 c)} \cdot \sqrt{3 a^{6} b^{2} c}$

Pull terms out from under the radical.

$a b^{2} \sqrt{6 c} \cdot \sqrt{3 a^{6} b^{2} c}$

Rewrite $3 a^{6} b^{2} c$ as ${(a^{3} b)}^{2} \cdot (3 c)$ .

Rewrite $a^{6}$ as ${(a^{3})}^{2}$ .

$a b^{2} \sqrt{6 c} \cdot \sqrt{3 {(a^{3})}^{2} b^{2} c}$

Move $3$ .

$a b^{2} \sqrt{6 c} \cdot \sqrt{{(a^{3})}^{2} b^{2} \cdot 3 c}$

Rewrite ${(a^{3})}^{2} b^{2}$ as ${(a^{3} b)}^{2}$ .

$a b^{2} \sqrt{6 c} \cdot \sqrt{{(a^{3} b)}^{2} \cdot 3 c}$

Add parentheses.

$a b^{2} \sqrt{6 c} \cdot \sqrt{{(a^{3} b)}^{2} \cdot (3 c)}$

Pull terms out from under the radical.

$a b^{2} \sqrt{6 c} \cdot (a^{3} b \sqrt{3 c})$

Multiply $a$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$a^{3} a b^{2} \sqrt{6 c} \cdot (b \sqrt{3 c})$

Multiply $a^{3}$ by $a$ .

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

$a^{3} a^{1} b^{2} \sqrt{6 c} \cdot (b \sqrt{3 c})$

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

$a^{3 + 1} b^{2} \sqrt{6 c} \cdot (b \sqrt{3 c})$

Add $3$ and $1$ .

$a^{4} b^{2} \sqrt{6 c} \cdot (b \sqrt{3 c})$

Multiply $b^{2}$ by $b$ by adding the exponents.

Move $b$ .

$a^{4} (b \cdot b^{2}) \sqrt{6 c} \cdot \sqrt{3 c}$

Multiply $b$ by $b^{2}$ .

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

$a^{4} (b^{1} b^{2}) \sqrt{6 c} \cdot \sqrt{3 c}$

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

$a^{4} b^{1 + 2} \sqrt{6 c} \cdot \sqrt{3 c}$

Add $1$ and $2$ .

$a^{4} b^{3} \sqrt{6 c} \cdot \sqrt{3 c}$

Multiply $a^{4} b^{3} \sqrt{6 c} \sqrt{3 c}$ .

Combine using the product rule for radicals.

$a^{4} b^{3} \sqrt{3 c (6 c)}$

Multiply $6$ by $3$ .

$a^{4} b^{3} \sqrt{18 c \cdot c}$

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

$a^{4} b^{3} \sqrt{18 (c^{1} c)}$

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

$a^{4} b^{3} \sqrt{18 (c^{1} c^{1})}$

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

$a^{4} b^{3} \sqrt{18 c^{1 + 1}}$

Add $1$ and $1$ .

$a^{4} b^{3} \sqrt{18 c^{2}}$

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

Factor $9$ out of $18$ .

$a^{4} b^{3} \sqrt{9 (2) c^{2}}$

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

$a^{4} b^{3} \sqrt{3^{2} \cdot 2 c^{2}}$

Move $2$ .

$a^{4} b^{3} \sqrt{3^{2} c^{2} \cdot 2}$

Rewrite $3^{2} c^{2}$ as ${(3 c)}^{2}$ .

$a^{4} b^{3} \sqrt{{(3 c)}^{2} \cdot 2}$

Pull terms out from under the radical.

$a^{4} b^{3} (3 c \sqrt{2})$

Rewrite using the commutative property of multiplication.

$3 \sqrt{2} a^{4} b^{3} c$

Simplify square root of 6a^2b^4c* square root of 3a^6b^2c

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