Simplify the Radical Expression ( square root of 44a^2b)/( square root of 11b^7c^4)

$\frac{\sqrt{44 a^{2} b}}{\sqrt{11 b^{7} c^{4}}}$

Step 1

Combine $\sqrt{44 a^{2} b}$ and $\sqrt{11 b^{7} c^{4}}$ into a single radical.

$\sqrt{\frac{44 a^{2} b}{11 b^{7} c^{4}}}$

Step 2

Reduce the expression $\frac{44 a^{2} b}{11 b^{7} c^{4}}$ by cancelling the common factors.

Factor $11$ out of $44 a^{2} b$ .

$\sqrt{\frac{11 (4 a^{2} b)}{11 b^{7} c^{4}}}$

Factor $11$ out of $11 b^{7} c^{4}$ .

$\sqrt{\frac{11 (4 a^{2} b)}{11 (b^{7} c^{4})}}$

Cancel the common factor.

$\sqrt{\frac{11 (4 a^{2} b)}{11 (b^{7} c^{4})}}$

Rewrite the expression.

$\sqrt{\frac{4 a^{2} b}{b^{7} c^{4}}}$

Step 3

Cancel the common factor of $b$ and $b^{7}$ .

Factor $b$ out of $4 a^{2} b$ .

$\sqrt{\frac{b (4 a^{2})}{b^{7} c^{4}}}$

Cancel the common factors.

Factor $b$ out of $b^{7} c^{4}$ .

$\sqrt{\frac{b (4 a^{2})}{b (b^{6} c^{4})}}$

Cancel the common factor.

$\sqrt{\frac{b (4 a^{2})}{b (b^{6} c^{4})}}$

Rewrite the expression.

$\sqrt{\frac{4 a^{2}}{b^{6} c^{4}}}$

Step 4

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

$\sqrt{\frac{{(2 a)}^{2}}{b^{6} c^{4}}}$

Step 5

Rewrite $b^{6} c^{4}$ as ${(b^{3} c^{2})}^{2}$ .

$\sqrt{\frac{{(2 a)}^{2}}{{(b^{3} c^{2})}^{2}}}$

Step 6

Rewrite $\frac{{(2 a)}^{2}}{{(b^{3} c^{2})}^{2}}$ as ${(\frac{2 a}{b^{3} c^{2}})}^{2}$ .

$\sqrt{{(\frac{2 a}{b^{3} c^{2}})}^{2}}$

Step 7

Pull terms out from under the radical.

$| \frac{2 a}{b^{3} c^{2}} |$

Step 8

Remove non-negative terms from the absolute value.

$\frac{2 | a |}{c^{2} | b^{3} |}$