Question

Use the product property of roots to choose the expression equivalent to 3√(5x) * 3√(25x)?

1) 3√(5x) * 3√(5x)
2) 3√(5x) * 3√(5x²)
3) 3√(5x) * 3√(25x²)
4) 3√(5x) * 3√(125x²)

Answer 1

To find the expression equivalent to 3√(5x) * 3√(25x), we use the product property of roots, which leads to 3√(5x) * 3√(5x2), option 2 being the correct answer.

Step-by-step explanation:

The product property of roots allows us to multiply the cube roots in the expression by combining the radicands (the numbers inside the radical sign) under a single radical. So when we multiply 3√(5x) by 3√(25x), we combine the radicands to get 3√(5x * 25x). Simplifying further, since 25x can be expressed as 52x, our expression becomes 3√(5x * 52x), which is option 2.