Simplify square root of 15b^3 square root of 30b^6

$\sqrt{15 b^{3}} \sqrt{30 b^{6}}$

Step 1

Rewrite $15 b^{3}$ as $b^{2} \cdot (15 b)$ .

Factor out $b^{2}$ .

$\sqrt{15 (b^{2} b)} \sqrt{30 b^{6}}$

Reorder $15$ and $b^{2}$ .

$\sqrt{b^{2} \cdot 15 b} \sqrt{30 b^{6}}$

Add parentheses.

$\sqrt{b^{2} \cdot (15 b)} \sqrt{30 b^{6}}$

Step 2

Pull terms out from under the radical.

$b \sqrt{15 b} \sqrt{30 b^{6}}$

Step 3

Rewrite $30 b^{6}$ as ${(b^{3})}^{2} \cdot 30$ .

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

$b \sqrt{15 b} \sqrt{30 {(b^{3})}^{2}}$

Reorder $30$ and ${(b^{3})}^{2}$ .

$b \sqrt{15 b} \sqrt{{(b^{3})}^{2} \cdot 30}$

Step 4

Pull terms out from under the radical.

$b \sqrt{15 b} (b^{3} \sqrt{30})$

Step 5

Rewrite using the commutative property of multiplication.

$\sqrt{30} b \sqrt{15 b} b^{3}$

Step 6

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

Move $b^{3}$ .

$\sqrt{30} (b^{3} b) \sqrt{15 b}$

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

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

$\sqrt{30} (b^{3} b^{1}) \sqrt{15 b}$

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

$\sqrt{30} b^{3 + 1} \sqrt{15 b}$

Add $3$ and $1$ .

$\sqrt{30} b^{4} \sqrt{15 b}$

Step 7

Multiply $\sqrt{30} b^{4} \sqrt{15 b}$ .

Combine using the product rule for radicals.

$b^{4} \sqrt{30 (15 b)}$

Multiply $30$ by $15$ .

$b^{4} \sqrt{450 b}$

Step 8

Rewrite $450 b$ as $15^{2} \cdot (2 b)$ .

Factor $225$ out of $450$ .

$b^{4} \sqrt{225 (2) b}$

Rewrite $225$ as $15^{2}$ .

$b^{4} \sqrt{15^{2} \cdot 2 b}$

Add parentheses.

$b^{4} \sqrt{15^{2} \cdot (2 b)}$

Step 9

Pull terms out from under the radical.

$b^{4} (15 \sqrt{2 b})$

Step 10

Rewrite using the commutative property of multiplication.

$15 b^{4} \sqrt{2 b}$

Simplify square root of 15b^3 square root of 30b^6

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