Algebra Examples

$\sqrt{6 x^{4}} \cdot 5 \sqrt{8 x^{5}}$

Step 1

Rewrite using the commutative property of multiplication.

$5 \sqrt{6 x^{4}} \sqrt{8 x^{5}}$

Step 2

Rewrite $6 x^{4}$ as ${(x^{2})}^{2} \cdot 6$ .

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Step 2.1

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

$5 \sqrt{6 {(x^{2})}^{2}} \sqrt{8 x^{5}}$

Step 2.2

Reorder $6$ and ${(x^{2})}^{2}$ .

$5 \sqrt{{(x^{2})}^{2} \cdot 6} \sqrt{8 x^{5}}$

Step 3

Pull terms out from under the radical.

$5 (x^{2} \sqrt{6}) \sqrt{8 x^{5}}$

Step 4

Rewrite $8 x^{5}$ as ${(2 x^{2})}^{2} \cdot (2 x)$ .

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Step 4.1

Factor $4$ out of $8$ .

$5 x^{2} \sqrt{6} \sqrt{4 (2) x^{5}}$

Step 4.2

Rewrite $4$ as $2^{2}$ .

$5 x^{2} \sqrt{6} \sqrt{2^{2} \cdot 2 x^{5}}$

Step 4.3

Factor out $x^{4}$ .

$5 x^{2} \sqrt{6} \sqrt{2^{2} \cdot 2 (x^{4} x)}$

Step 4.4

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

$5 x^{2} \sqrt{6} \sqrt{2^{2} \cdot 2 ({(x^{2})}^{2} x)}$

Step 4.5

Move $2$ .

$5 x^{2} \sqrt{6} \sqrt{2^{2} {(x^{2})}^{2} \cdot 2 x}$

Step 4.6

Rewrite $2^{2} {(x^{2})}^{2}$ as ${(2 x^{2})}^{2}$ .

$5 x^{2} \sqrt{6} \sqrt{{(2 x^{2})}^{2} \cdot 2 x}$

Step 4.7

Add parentheses.

$5 x^{2} \sqrt{6} \sqrt{{(2 x^{2})}^{2} \cdot (2 x)}$

Step 5

Pull terms out from under the radical.

$5 x^{2} \sqrt{6} (2 x^{2} \sqrt{2 x})$

Step 6

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 6.1

Move $x^{2}$ .

$5 (x^{2} x^{2}) \sqrt{6} (2 \sqrt{2 x})$

Step 6.2

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

$5 x^{2 + 2} \sqrt{6} (2 \sqrt{2 x})$

Step 6.3

Add $2$ and $2$ .

$5 x^{4} \sqrt{6} (2 \sqrt{2 x})$

Step 7

Multiply $5 x^{4} \sqrt{6} (2 \sqrt{2 x})$ .

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Step 7.1

Multiply $2$ by $5$ .

$10 x^{4} \sqrt{6} \sqrt{2 x}$

Step 7.2

Combine using the product rule for radicals.

$10 x^{4} \sqrt{2 x \cdot 6}$

Step 7.3

Multiply $6$ by $2$ .

$10 x^{4} \sqrt{12 x}$

Step 8

Rewrite $12 x$ as $2^{2} \cdot (3 x)$ .

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Step 8.1

Factor $4$ out of $12$ .

$10 x^{4} \sqrt{4 (3) x}$

Step 8.2

Rewrite $4$ as $2^{2}$ .

$10 x^{4} \sqrt{2^{2} \cdot 3 x}$

Step 8.3

Add parentheses.

$10 x^{4} \sqrt{2^{2} \cdot (3 x)}$

Step 9

Pull terms out from under the radical.

$10 x^{4} (2 \sqrt{3 x})$

Step 10

Multiply $2$ by $10$ .

$20 x^{4} \sqrt{3 x}$