Question

What choice is equivalent to the quotient when x>0? [Photo attached]

Answer 1

Answer:

$\Large \boxed{\bold{D.} \ \frac{5 \sqrt{x} } {4}}$

Step-by-step explanation:

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

Distributing the square root.

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

Simplifying the expression.

$\displaystyle \frac{5 \cdot \sqrt{2} \cdot x \cdot \sqrt{x} } {4 \cdot \sqrt{2} \cdot x}$

Cancelling the square root of 2 and x on both the numerator and the denominator.

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

Answer 2

Answer:

D)  5√x / 4

Step-by-step explanation:

√50x^3 / √32x^2

= (5x√2x) / (4x√2)

= 5/4 √(2x/2)

= 5/4 (√x)

= 5√x / 4