Simplify (24 square root of 225x^22)/(4 square root of 5x^4)

$\frac{24 \sqrt{225 x^{22}}}{4 \sqrt{5 x^{4}}}$

Step 1

Cancel the common factor of $24$ and $4$ .

Factor $4$ out of $24 \sqrt{225 x^{22}}$ .

$\frac{4 (6 \sqrt{225 x^{22}})}{4 \sqrt{5 x^{4}}}$

Cancel the common factors.

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

$\frac{4 (6 \sqrt{225 x^{22}})}{4 (\sqrt{5 x^{4}})}$

Cancel the common factor.

$\frac{4 (6 \sqrt{225 x^{22}})}{4 \sqrt{5 x^{4}}}$

Rewrite the expression.

$\frac{6 \sqrt{225 x^{22}}}{\sqrt{5 x^{4}}}$

Step 2

Combine $\sqrt{225 x^{22}}$ and $\sqrt{5 x^{4}}$ into a single radical.

$6 \sqrt{\frac{225 x^{22}}{5 x^{4}}}$

Step 3

Reduce the expression $\frac{225 x^{22}}{5 x^{4}}$ by cancelling the common factors.

Factor $5$ out of $225 x^{22}$ .

$6 \sqrt{\frac{5 (45 x^{22})}{5 x^{4}}}$

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

$6 \sqrt{\frac{5 (45 x^{22})}{5 (x^{4})}}$

Cancel the common factor.

$6 \sqrt{\frac{5 (45 x^{22})}{5 x^{4}}}$

Rewrite the expression.

$6 \sqrt{\frac{45 x^{22}}{x^{4}}}$

Step 4

Cancel the common factor of $x^{22}$ and $x^{4}$ .

Factor $x^{4}$ out of $45 x^{22}$ .

$6 \sqrt{\frac{x^{4} (45 x^{18})}{x^{4}}}$

Cancel the common factors.

Multiply by $1$ .

$6 \sqrt{\frac{x^{4} (45 x^{18})}{x^{4} \cdot 1}}$

Cancel the common factor.

$6 \sqrt{\frac{x^{4} (45 x^{18})}{x^{4} \cdot 1}}$

Rewrite the expression.

$6 \sqrt{\frac{45 x^{18}}{1}}$

Divide $45 x^{18}$ by $1$ .

$6 \sqrt{45 x^{18}}$

Step 5

Rewrite $45 x^{18}$ as ${(3 x^{9})}^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$6 \sqrt{9 (5) x^{18}}$

Rewrite $9$ as $3^{2}$ .

$6 \sqrt{3^{2} \cdot 5 x^{18}}$

Rewrite $x^{18}$ as ${(x^{9})}^{2}$ .

$6 \sqrt{3^{2} \cdot 5 {(x^{9})}^{2}}$

Move $5$ .

$6 \sqrt{3^{2} {(x^{9})}^{2} \cdot 5}$

Rewrite $3^{2} {(x^{9})}^{2}$ as ${(3 x^{9})}^{2}$ .

$6 \sqrt{{(3 x^{9})}^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

$6 (3 x^{9} \sqrt{5})$

Step 7

Multiply $3$ by $6$ .

$18 x^{9} \sqrt{5}$

Simplify (24 square root of 225x^22)/(4 square root of 5x^4)

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