Final answer:
The given equation involves multiplying radicals and combining like terms. Simplifying the expressions, we end up with an expression that does not exactly match any of the provided options. Making an approximate assumption for √(15), the closest option is 8b7/2.
Step-by-step explanation:
To solve the equation √(24b³) × √(40b²) × √(b²), we first need to multiply the radical expressions together. Applying the property of radicals that √(a) × √(b) = √(ab), we can combine the three under a single radical. Thus, we get √(24b³ × 40b² × b²).
Next, we multiply the numbers and combine the like terms for the exponents of b. We have 24 × 40 = 960 and b³ × b² × b² = b3+2+2 = b7. So, the expression simplifies to √(960b7). Since 960 = 64 × 15 and 64 is a perfect square, we further simplify it to √(64) × √(15b7), which equals 8b3 × √(15b7). However, noticing that b7 can be written as (b6)(b), where b6 is a perfect square since 6 is an even exponent, we get 8b3 × √(15)×√(b6)×√(b).
Finally, we know √(b6) = b6/2 = b3 and √(b) = b1/2. The expression simplifies to 8b3 × b3 × b1/2 × √(15), giving us a result of 8b7/2 × √(15). As no option matches this result, we conclude there might be a mistake in the question or in the provided options. But, the closest matching option with a minor assumption of √(15) approximately equal to 4 (which is not accurate) is option d) 8b7/2.