Simplify square root of 21b square root of 35b

$\sqrt{21 b} \sqrt{35 b}$

Step 1

Multiply $\sqrt{21 b} \sqrt{35 b}$ .

Combine using the product rule for radicals.

$\sqrt{21 b (35 b)}$

Multiply $35$ by $21$ .

$\sqrt{735 b \cdot b}$

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

$\sqrt{735 (b^{1} b)}$

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

$\sqrt{735 (b^{1} b^{1})}$

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

$\sqrt{735 b^{1 + 1}}$

Add $1$ and $1$ .

$\sqrt{735 b^{2}}$

Step 2

Rewrite $735 b^{2}$ as ${(7 b)}^{2} \cdot 15$ .

Factor $49$ out of $735$ .

$\sqrt{49 (15) b^{2}}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 15 b^{2}}$

Move $15$ .

$\sqrt{7^{2} b^{2} \cdot 15}$

Rewrite $7^{2} b^{2}$ as ${(7 b)}^{2}$ .

$\sqrt{{(7 b)}^{2} \cdot 15}$

Step 3

Pull terms out from under the radical.

$7 b \sqrt{15}$