Question

which choice is equivalent to the expression below when y≥0? √y^3+✓4y^3-2y√y

the answer was y√y

Answer 1

Answer:

$y \sqrt{y}$

Step-by-step explanation:

The given expresion is

$\sqrt{ {y}^{3} } + \sqrt{4 {y}^{3} } - 2y \sqrt{y}$

We need to simplify the first two terms by removing the perfect squares under the radical sign.

$\sqrt{ {y}^{2} \times y} + \sqrt{4 {y}^{2} \times y } - 2y \sqrt{y}$

$y \sqrt{y} + 2y \sqrt{y} - 2y \sqrt{y}$

The last two terms zero pairs, they will simplify to zero.

$y \sqrt{y} + 0$

The final answer is

$y \sqrt{y}$