Algebra Examples

$\sqrt{5 x^{5}} \cdot \sqrt{10 a^{2}}$

Step 1

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

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Step 1.1

Factor out $x^{4}$ .

$\sqrt{5 (x^{4} x)} \cdot \sqrt{10 a^{2}}$

Step 1.2

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

$\sqrt{5 ({(x^{2})}^{2} x)} \cdot \sqrt{10 a^{2}}$

Step 1.3

Reorder $5$ and ${(x^{2})}^{2}$ .

$\sqrt{{(x^{2})}^{2} \cdot 5 x} \cdot \sqrt{10 a^{2}}$

Step 1.4

Add parentheses.

$\sqrt{{(x^{2})}^{2} \cdot (5 x)} \cdot \sqrt{10 a^{2}}$

Step 2

Pull terms out from under the radical.

$x^{2} \sqrt{5 x} \cdot \sqrt{10 a^{2}}$

Step 3

Reorder $10$ and $a^{2}$ .

$x^{2} \sqrt{5 x} \cdot \sqrt{a^{2} \cdot 10}$

Step 4

Pull terms out from under the radical.

$x^{2} \sqrt{5 x} \cdot (a \sqrt{10})$

Step 5

Rewrite using the commutative property of multiplication.

$\sqrt{10} x^{2} \sqrt{5 x} a$

Step 6

Multiply $\sqrt{10} x^{2} \sqrt{5 x}$ .

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Step 6.1

Combine using the product rule for radicals.

$x^{2} \sqrt{10 (5 x)} a$

Step 6.2

Multiply $10$ by $5$ .

$x^{2} \sqrt{50 x} a$

Step 7

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

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Step 7.1

Factor $25$ out of $50$ .

$x^{2} \sqrt{25 (2) x} a$

Step 7.2

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

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

Step 7.3

Add parentheses.

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

Step 8

Pull terms out from under the radical.

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

Step 9

Rewrite using the commutative property of multiplication.

$5 x^{2} \sqrt{2 x} a$