Final answer:
Yes, it is possible to write 4√y³/√y as a single radical by expressing the radicals as fractional powers, simplifying the expression by dividing the exponents, and then reverting back to the radical form.
Step-by-step explanation:
The question asks whether it is possible to simplify the expression 4√y³/√y into a single radical despite having different indices. By using properties of exponents, we can express both radicals with the same index and simplify the division inside the same radical.
Firstly, we express the radicals as fractional exponents. The expression can be rewritten as y³²/y¹². Since the bases are the same, we can subtract the exponents according to the quotient rule for exponents: (y³/y¹)¹², which simplifies to y²². Thus, we can indeed write the original expression as a single radical, which in simplest form is √y² or just y.