Trigonometry Examples

$\frac{\sqrt{40 x^{5}}}{\sqrt{10 x}}$

Step 1

Combine $\sqrt{40 x^{5}}$ and $\sqrt{10 x}$ into a single radical.

$\sqrt{\frac{40 x^{5}}{10 x}}$

Step 2

Reduce the expression $\frac{40 x^{5}}{10 x}$ by cancelling the common factors.

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Step 2.1

Factor $10$ out of $40 x^{5}$ .

$\sqrt{\frac{10 (4 x^{5})}{10 x}}$

Step 2.2

Factor $10$ out of $10 x$ .

$\sqrt{\frac{10 (4 x^{5})}{10 (x)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{10 (4 x^{5})}{10 x}}$

Step 2.4

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{5}$ and $x$ .

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Step 3.1

Factor $x$ out of $4 x^{5}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt{\frac{x (4 x^{4})}{x^{1}}}$

Step 3.2.2

Factor $x$ out of $x^{1}$ .

$\sqrt{\frac{x (4 x^{4})}{x \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$\sqrt{\frac{x (4 x^{4})}{x \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$\sqrt{\frac{4 x^{4}}{1}}$

Step 3.2.5

Divide $4 x^{4}$ by $1$ .

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

Step 4

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

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

Step 5

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

$2 x^{2}$