Video Explanation

Text Explanation

This problem explores the properties of roots.  In addition to the video lessons below, here's a GMAT blog on the topic. 

We can separate roots by multiplication

This allows us to separate the prompt into three
different factors: 

By doing this, we really break the problem into three separate problems.  We just have to find each one of those roots separately, and then take the product. 

The number 72 is not a perfect square, but it is divisible by a perfect square.  We take advantage of the same "separation by multiplication" property above, as described in this GMAT post. 

We will follow this exact same procedure to take the square root of x³. 

In some ways, the real "trap" part of
the problem concerns taking the square root of y¹⁶.  First of all, recognize that rules for what
you do with exponents are always different from what they are
for ordinary numbers.  We know with
ordinary numbers

and from that fact alone, we are guaranteed that whatever the square root of y¹⁶ is, it can't possibly be y⁴.  That is guaranteed to be a trap answer. 

Taking
the square root of something is the same as raising it to the power of
1/2.  When we have a power to a power, we
use the exponent rule:

In other words, exponentiating a power means
multiply the exponents.  Here:

One way to see why this is true --- whatever the
square root of y¹⁶ equals, it must be the thing that, when
multiplied by itself, equals y¹⁶. 
Clearly,

so this necessary means that y⁸ is the square root of y¹⁶. 

Now,
we have all three roots, so we can combine them. 

Answer = C