Algebra Examples

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

Step 1

Pull terms out from under the radical.

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

Step 2

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

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Step 2.1

Multiply $3$ by $2$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Add $1$ and $1$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Rewrite the expression.

$6 a b^{1}$

Step 3.5

Simplify.

$6 a b$