Algebra Examples

$\frac{\sqrt{25 x^{3}}}{\sqrt{4}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $25 x^{3}$ as ${(5 x)}^{2} x$ .

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Step 1.1.1

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

$\frac{\sqrt{5^{2} x^{3}}}{\sqrt{4}}$

Step 1.1.2

Factor out $x^{2}$ .

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

Step 1.1.3

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

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

Step 1.2

Pull terms out from under the radical.

$\frac{5 x \sqrt{x}}{\sqrt{4}}$

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{5 x \sqrt{x}}{2}$