Question

What is the following product? Assume y≥0

√y^3 * √y^3

y^3

2y^3

y^6

2y^6

Answer 1

We are asked to calculate the product:

$\sqrt{y^3} \cdot \sqrt{y^3}$

By rewriting the square roots as a power, we can easily solve the expression, in fact:

$=(y^3)^{\frac{1}{2}} \cdot (y^3)^{\frac{1}{2}} = (y^3)^{\frac{1}{2}+\frac{1}{2}}=(y^3 )^{1} =y^3$

so, the correct answer is A) $y^3$

Answer 2

Answer: The first option: y^3

Explanation: Here we need to use some relations:

$x^{a}*x^{b}  = x^{a + b}$

and

$\sqrt[a]{x} = x^{1/a}$

then, the product:

√y^3 * √y^3

may be written as:

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

So the right option is the second one.