Question

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

Answer 1

`\Large \boxed{\bold{D.} \ \frac{5 √(x) } {4}}`

Explanation:

`\displaystyle (√(50x^3 ))/(√(32x^2 ) )`

Distributing the square root.

`\displaystyle \frac{√(50) √(x^3 ) } {√(32) √(x^2 )}`

Simplifying the expression.

`\displaystyle \frac{5 \cdot √(2) \cdot x \cdot √(x) } {4 \cdot √(2) \cdot x}`

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

`\displaystyle \frac{5 \cdot √(x) } {4}`

Answer 2

D) 5√x / 4

Explanation:

√50x^3 / √32x^2

= (5x√2x) / (4x√2)

= 5/4 √(2x/2)

= 5/4 (√x)

= 5√x / 4