Simplify ( square root of 50x^3)÷( square root of 32x^2)

$\sqrt{50 x^{3}} \div \sqrt{32 x^{2}}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{50 x^{3}}}{\sqrt{32 x^{2}}}$

Step 2

Combine $\sqrt{50 x^{3}}$ and $\sqrt{32 x^{2}}$ into a single radical.

$\sqrt{\frac{50 x^{3}}{32 x^{2}}}$

Step 3

Reduce the expression $\frac{50 x^{3}}{32 x^{2}}$ by cancelling the common factors.

Factor $2$ out of $50 x^{3}$ .

$\sqrt{\frac{2 (25 x^{3})}{32 x^{2}}}$

Factor $2$ out of $32 x^{2}$ .

$\sqrt{\frac{2 (25 x^{3})}{2 (16 x^{2})}}$

Cancel the common factor.

$\sqrt{\frac{2 (25 x^{3})}{2 (16 x^{2})}}$

Rewrite the expression.

$\sqrt{\frac{25 x^{3}}{16 x^{2}}}$

Step 4

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $25 x^{3}$ .

$\sqrt{\frac{x^{2} (25 x)}{16 x^{2}}}$

Cancel the common factors.

Factor $x^{2}$ out of $16 x^{2}$ .

$\sqrt{\frac{x^{2} (25 x)}{x^{2} \cdot 16}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (25 x)}{x^{2} \cdot 16}}$

Rewrite the expression.

$\sqrt{\frac{25 x}{16}}$

Step 5

Rewrite $\frac{25 x}{16}$ as ${(\frac{5}{4})}^{2} x$ .

Factor the perfect power $5^{2}$ out of $25 x$ .

$\sqrt{\frac{5^{2} x}{16}}$

Factor the perfect power $4^{2}$ out of $16$ .

$\sqrt{\frac{5^{2} x}{4^{2} \cdot 1}}$

Rearrange the fraction $\frac{5^{2} x}{4^{2} \cdot 1}$ .

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

Step 6

Pull terms out from under the radical.

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

Step 7

Combine $\frac{5}{4}$ and $\sqrt{x}$ .

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