Algebra Examples

$\sqrt{\frac{96 d^{4} e^{2} f^{8}}{75 d e^{6}}}$

Step 1

Reduce the expression $\frac{96 d^{4} e^{2} f^{8}}{75 d e^{6}}$ by cancelling the common factors.

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Step 1.1

Factor $3$ out of $96 d^{4} e^{2} f^{8}$ .

$\sqrt{\frac{3 (32 d^{4} e^{2} f^{8})}{75 d e^{6}}}$

Step 1.2

Factor $3$ out of $75 d e^{6}$ .

$\sqrt{\frac{3 (32 d^{4} e^{2} f^{8})}{3 (25 d e^{6})}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{3 (32 d^{4} e^{2} f^{8})}{3 (25 d e^{6})}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{32 d^{4} e^{2} f^{8}}{25 d e^{6}}}$

Step 2

Cancel the common factor of $d^{4}$ and $d$ .

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Step 2.1

Factor $d$ out of $32 d^{4} e^{2} f^{8}$ .

$\sqrt{\frac{d (32 d^{3} e^{2} f^{8})}{25 d e^{6}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $d$ out of $25 d e^{6}$ .

$\sqrt{\frac{d (32 d^{3} e^{2} f^{8})}{d (25 e^{6})}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{d (32 d^{3} e^{2} f^{8})}{d (25 e^{6})}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{32 d^{3} e^{2} f^{8}}{25 e^{6}}}$

Step 3

Cancel the common factor of $e^{2}$ and $e^{6}$ .

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Step 3.1

Factor $e^{2}$ out of $32 d^{3} e^{2} f^{8}$ .

$\sqrt{\frac{e^{2} (32 d^{3} f^{8})}{25 e^{6}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $e^{2}$ out of $25 e^{6}$ .

$\sqrt{\frac{e^{2} (32 d^{3} f^{8})}{e^{2} (25 e^{4})}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{e^{2} (32 d^{3} f^{8})}{e^{2} (25 e^{4})}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{32 d^{3} f^{8}}{25 e^{4}}}$

Step 4

Rewrite $\frac{32 d^{3} f^{8}}{25 e^{4}}$ as ${(\frac{4 d f^{4}}{5 e^{2}})}^{2} (2 d)$ .

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Step 4.1

Factor the perfect power ${(4 d f^{4})}^{2}$ out of $32 d^{3} f^{8}$ .

$\sqrt{\frac{{(4 d f^{4})}^{2} \cdot (2 d)}{25 e^{4}}}$

Step 4.2

Factor the perfect power ${(5 e^{2})}^{2}$ out of $25 e^{4}$ .

$\sqrt{\frac{{(4 d f^{4})}^{2} \cdot (2 d)}{{(5 e^{2})}^{2} \cdot 1}}$

Step 4.3

Rearrange the fraction $\frac{{(4 d f^{4})}^{2} \cdot (2 d)}{{(5 e^{2})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{4 d f^{4}}{5 e^{2}})}^{2} (2 d)}$

Step 5

Pull terms out from under the radical.

$\frac{4 d f^{4}}{5 e^{2}} \sqrt{2 d}$

Step 6

Combine $\frac{4 d f^{4}}{5 e^{2}}$ and $\sqrt{2 d}$ .

$\frac{4 d f^{4} \sqrt{2 d}}{5 e^{2}}$