Simplify (2 square root of a^2b)(3 square root of b)

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

Step 1

Pull terms out from under the radical.

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

Step 2

Multiply $2 a \sqrt{b} (3 \sqrt{b})$ .

Multiply $3$ by $2$ .

$6 a \sqrt{b} \sqrt{b}$

Raise $\sqrt{b}$ to the power of $1$ .

$6 a ({\sqrt{b}}^{1} \sqrt{b})$

Raise $\sqrt{b}$ to the power of $1$ .

$6 a ({\sqrt{b}}^{1} {\sqrt{b}}^{1})$

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

$6 a {\sqrt{b}}^{1 + 1}$

Add $1$ and $1$ .

$6 a {\sqrt{b}}^{2}$

Step 3

Rewrite ${\sqrt{b}}^{2}$ as $b$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{b}$ as $b^{\frac{1}{2}}$ .

$6 a {(b^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$6 a b^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$6 a b^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$6 a b^{\frac{2}{2}}$

Rewrite the expression.

$6 a b^{1}$

Simplify.

$6 a b$