Question

Which choice is equivalent to the expression below when y2 0? √y^2 + √16y^3 – 4y√y

Answer 1

Answer:

Option C.

Step-by-step explanation:

We start with the expression:

$\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y}$

where y > 0. (this allow us to have y inside a square root, so we don't mess with complex numbers)

We want to find the equivalent expression to this one.

Here, we can do the next two simplifications:

$\sqrt{16*y^3} = \sqrt{16} \sqrt{y^3} = 4*\sqrt{y^3}$

And:

$y*\sqrt{y} = \sqrt{y^2} *\sqrt{y} = \sqrt{y^2*y} = \sqrt{y^3}$

If we apply these two to our initial expression, we can rewrite it as:

$\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y}$

$\sqrt{y^3} + 4*\sqrt{y^3} - 4\sqrt{y^3} = \sqrt{y^3}$

Here we can use the second simplification again, to rewrite:

$\sqrt{y^3} = y*\sqrt{y}$

So, concluding, we have:

$\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y} = y*\sqrt{y}$

Then the correct option is C.