Question

Which choice is equivalent to the expression below when y is greater than or equal to zero? √(y³) √(4y³) -

1) √(y³) - √(4y³)
2) √(y³) + √(4y³)
3) √(y³) * √(4y³)
4) √(y³) / √(4y³)

Answer 1

None of the options provided are equivalent to the original expression \(\sqrt{y^3}\) when y is greater than or equal to zero. After simplifying option 4, which is the division option, we can conclude that it does not equal \(\sqrt{y^3}\). The other options involve operations that introduce additional terms to the expression.

Step-by-step explanation:

The student has asked which choice is equivalent to the expression \(\sqrt{y^3}\) when y \geq 0. To solve this, we need to simplify the given options and determine which one equals \(\sqrt{y^3}\).

1. \(\sqrt{y^3}\) \(\sqrt{4y^3} - 1\)
2. \(\sqrt{y^3}\) - \(\sqrt{4y^3}\)
3. \(\sqrt{y^3}\) + \(\sqrt{4y^3}\)
4. \(\sqrt{y^3}\) \(\sqrt{4y^3}\)

Upon examination, we see that option 4, \(\sqrt{y^3} / \sqrt{4y^3}\), simplifies to \(\sqrt{1/4}\) or \(1/2\) which is not equivalent to the original expression \(\sqrt{y^3}\). Options 1, 2, and 3 are operations on \(\sqrt{y^3}\) with another term and therefore cannot be equivalent to \(\sqrt{y^3}\) alone.

None of the options presented are equivalent to the original expression \(\sqrt{y^3}\) when y \geq 0.