Pre-Algebra Examples

$\sqrt{5 b^{3}} \sqrt{10 c^{4}}$

Step 1

Rewrite $5 b^{3}$ as $b^{2} \cdot (5 b)$ .

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Step 1.1

Factor out $b^{2}$ .

$\sqrt{5 (b^{2} b)} \sqrt{10 c^{4}}$

Step 1.2

Reorder $5$ and $b^{2}$ .

$\sqrt{b^{2} \cdot 5 b} \sqrt{10 c^{4}}$

Step 1.3

Add parentheses.

$\sqrt{b^{2} \cdot (5 b)} \sqrt{10 c^{4}}$

$\sqrt{b^{2} \cdot (5 b)} \sqrt{10 c^{4}}$

Step 2

Pull terms out from under the radical.

$b \sqrt{5 b} \sqrt{10 c^{4}}$

Step 3

Rewrite $10 c^{4}$ as ${(c^{2})}^{2} \cdot 10$ .

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Step 3.1

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

$b \sqrt{5 b} \sqrt{10 {(c^{2})}^{2}}$

Step 3.2

Reorder $10$ and ${(c^{2})}^{2}$ .

$b \sqrt{5 b} \sqrt{{(c^{2})}^{2} \cdot 10}$

$b \sqrt{5 b} \sqrt{{(c^{2})}^{2} \cdot 10}$

Step 4

Pull terms out from under the radical.

$b \sqrt{5 b} (c^{2} \sqrt{10})$

Step 5

Rewrite using the commutative property of multiplication.

$\sqrt{10} b \sqrt{5 b} c^{2}$

Step 6

Multiply $\sqrt{10} b \sqrt{5 b}$ .

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Step 6.1

Combine using the product rule for radicals.

$b \sqrt{10 (5 b)} c^{2}$

Step 6.2

Multiply $10$ by $5$ .

$b \sqrt{50 b} c^{2}$

$b \sqrt{50 b} c^{2}$

Step 7

Rewrite $50 b$ as $5^{2} \cdot (2 b)$ .

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Step 7.1

Factor $25$ out of $50$ .

$b \sqrt{25 (2) b} c^{2}$

Step 7.2

Rewrite $25$ as $5^{2}$ .

$b \sqrt{5^{2} \cdot 2 b} c^{2}$

Step 7.3

Add parentheses.

$b \sqrt{5^{2} \cdot (2 b)} c^{2}$

$b \sqrt{5^{2} \cdot (2 b)} c^{2}$

Step 8

Pull terms out from under the radical.

$b (5 \sqrt{2 b}) c^{2}$

Step 9

Rewrite using the commutative property of multiplication.

$5 b \sqrt{2 b} c^{2}$

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