Simplify square root of 2ab^2* square root of 10a^5b

$\sqrt{2 a b^{2}} \cdot \sqrt{10 a^{5} b}$

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

Move $a$ .

$\sqrt{2 b^{2} a} \cdot \sqrt{10 a^{5} b}$

Reorder $2$ and $b^{2}$ .

$\sqrt{b^{2} \cdot 2 a} \cdot \sqrt{10 a^{5} b}$

Add parentheses.

$\sqrt{b^{2} \cdot (2 a)} \cdot \sqrt{10 a^{5} b}$

Pull terms out from under the radical.

$b \sqrt{2 a} \cdot \sqrt{10 a^{5} b}$

Rewrite $10 a^{5} b$ as ${(a^{2})}^{2} \cdot (10 a b)$ .

Factor out $a^{4}$ .

$b \sqrt{2 a} \cdot \sqrt{10 (a^{4} a) b}$

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

$b \sqrt{2 a} \cdot \sqrt{10 ({(a^{2})}^{2} a) b}$

Reorder $10$ and ${(a^{2})}^{2}$ .

$b \sqrt{2 a} \cdot \sqrt{{(a^{2})}^{2} \cdot 10 a b}$

Add parentheses.

$b \sqrt{2 a} \cdot \sqrt{{(a^{2})}^{2} \cdot 10 (a b)}$

Add parentheses.

$b \sqrt{2 a} \cdot \sqrt{{(a^{2})}^{2} \cdot (10 a b)}$

Pull terms out from under the radical.

$b \sqrt{2 a} \cdot (a^{2} \sqrt{10 a b})$

Multiply $b \sqrt{2 a} (a^{2} \sqrt{10 a b})$ .

Combine using the product rule for radicals.

$b (a^{2} \sqrt{2 a (10 a b)})$

Multiply $10$ by $2$ .

$b (a^{2} \sqrt{20 a (a b)})$

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

$b (a^{2} \sqrt{20 (a^{1} a) b})$

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

$b (a^{2} \sqrt{20 (a^{1} a^{1}) b})$

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

$b (a^{2} \sqrt{20 a^{1 + 1} b})$

Add $1$ and $1$ .

$b (a^{2} \sqrt{20 a^{2} b})$

Rewrite $20 a^{2} b$ as ${(2 a)}^{2} \cdot (5 b)$ .

Factor $4$ out of $20$ .

$b (a^{2} \sqrt{4 (5) a^{2} b})$

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

$b (a^{2} \sqrt{2^{2} \cdot 5 a^{2} b})$

Move $5$ .

$b (a^{2} \sqrt{2^{2} a^{2} \cdot 5 b})$

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

$b (a^{2} \sqrt{{(2 a)}^{2} \cdot 5 b})$

Add parentheses.

$b (a^{2} \sqrt{{(2 a)}^{2} \cdot (5 b)})$

Pull terms out from under the radical.

$b (a^{2} (2 a \sqrt{5 b}))$

Rewrite using the commutative property of multiplication.

$2 b (a^{2} a \sqrt{5 b})$

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

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

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

$2 b (a^{2} a^{1} \sqrt{5 b})$

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

$2 b (a^{2 + 1} \sqrt{5 b})$

Add $2$ and $1$ .

$2 b (a^{3} \sqrt{5 b})$

$2 b a^{3} \sqrt{5 b}$

Simplify square root of 2ab^2* square root of 10a^5b

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