Question

What is the following product? Assume y≥0

√y^3 * √y^3

y^3

2y^3

y^6

2y^6

Answer 1

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:

`√(y^3)*√(y^3) =y^(3/2)*y^(3/2) = y^(3/2 + 3/2)   = y^3`

So the right option is the second one.

Answer 2

We are asked to calculate the product:

`√(y^3) \cdot √(y^3)`

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

`=(y^3)^{(1)/(2)} \cdot (y^3)^{(1)/(2)} = (y^3)^{(1)/(2)+(1)/(2)}=(y^3 )^(1) =y^3`

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