Algebra Examples

$\sqrt{a^{3} b} \sqrt{a b^{4}}$

Step 1

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

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Step 1.1

Factor out $a^{2}$ .

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

Step 1.2

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

Combine using the product rule for radicals.

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

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

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

Step 5.5

Add $1$ and $1$ .

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $a$ by $a$ by adding the exponents.

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Step 7.1

Move $a$ .

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

Step 7.2

Multiply $a$ by $a$ .

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$