Final answer:
To find the product of √bx and √b, we multiply under the square root to get √(bx × b) which simplifies to √b²√x, and because b is non-negative, the simplified product is bx.
Step-by-step explanation:
The student has asked what the product of √bx and √b, assuming b ≥ 0, is. To find the product of two square roots, we can multiply the numbers under the square root symbols if they are of the same index. In this case, we have:
- √bx × √b = √(bx × b) = √(b²x) = √b²√x
- Since we know that √b² is just b, we can simplify the expression to: √b×√x = b√x
- And because b is assumed to be non-negative, we can further simplify to: b√x = bx
Thus, the correct product is bx.