Final answer:
The simplified form of √(40b³) is 2b√(10), by factoring out the square roots of 2² and b², leaving the cube root of b inside the radical.
Step-by-step explanation:
The simplified form of √(40b³) can be found by factoring the radicand (the number inside the radical) into its prime factors and simplifying. Since 40 is 2² × 10 and we can write b³ as b² × b, the expression becomes √(2² × 10 × b² × b).
We can pull out the squares from under the radical, which gives us √(2²)√(10)√(b²)√(b), simplifying to 2b√(10) × √(b). Since there's no further simplification for √(b), the answer is 2b√(10), which corresponds to option A).