Simplify 6 square root of 3ab*4 square root of 24ab^3

$6 \sqrt{3 a b} \cdot 4 \sqrt{24 a b^{3}}$

Rewrite $24 a b^{3}$ as ${(2 b)}^{2} \cdot (6 a b)$ .

Factor $4$ out of $24$ .

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

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

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

Factor out $b^{2}$ .

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

Move $a$ .

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

Move $6$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $4$ .

$6 \sqrt{3 a b} \cdot (8 (b \sqrt{6 a b}))$

Multiply $6 \sqrt{3 a b} (8 b \sqrt{6 a b})$ .

Multiply $8$ by $6$ .

$48 \sqrt{3 a b} (b \sqrt{6 a b})$

Combine using the product rule for radicals.

$48 (b \sqrt{3 a b (6 a b)})$

Multiply $6$ by $3$ .

$48 (b \sqrt{18 a b (a b)})$

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

$48 (b \sqrt{18 (a^{1} a) b \cdot b})$

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

$48 (b \sqrt{18 (a^{1} a^{1}) b \cdot b})$

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

$48 (b \sqrt{18 a^{1 + 1} b \cdot b})$

Add $1$ and $1$ .

$48 (b \sqrt{18 a^{2} b \cdot b})$

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

$48 (b \sqrt{18 a^{2} (b^{1} b)})$

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

$48 (b \sqrt{18 a^{2} (b^{1} b^{1})})$

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

$48 (b \sqrt{18 a^{2} b^{1 + 1}})$

Add $1$ and $1$ .

$48 (b \sqrt{18 a^{2} b^{2}})$

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

Factor $9$ out of $18$ .

$48 (b \sqrt{9 (2) a^{2} b^{2}})$

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

$48 (b \sqrt{3^{2} \cdot 2 a^{2} b^{2}})$

Move $2$ .

$48 (b \sqrt{3^{2} a^{2} b^{2} \cdot 2})$

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

$48 (b \sqrt{{(3 a b)}^{2} \cdot 2})$

Pull terms out from under the radical.

$48 (b (3 a b \sqrt{2}))$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$48 (b \cdot b (3 a \sqrt{2}))$

Multiply $b$ by $b$ .

$48 (b^{2} (3 a \sqrt{2}))$

Rewrite using the commutative property of multiplication.

$48 (3 \sqrt{2} b^{2} a)$

Multiply $3$ by $48$ .

$144 \sqrt{2} b^{2} a$

Simplify 6 square root of 3ab*4 square root of 24ab^3

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