Final answer:
The expression 6¹⁄₂ + 6³⁄₂ simplifies to 7√6, since 6¹⁄₂ is √6 and 6³⁄₂ is √6², which equals 6. Therefore, the correct answer is B. 7√6.
Step-by-step explanation:
The question involves evaluating the expression 6¹⁄₂ + 6³⁄₂. To do this, we need to understand that exponents written as fractions indicate roots. In this case, 6¹⁄₂ represents the square root of 6 (√6), and 6³⁄₂ represents the cube root of 6 squared (√6² or 6³⁄₂ = 6). Therefore, the expression can be simplified as follows:
√6 + 6
Now, let's add together these two terms:
√6 + 6 = √6 + √36
Since √36 = 6, the expression simplifies further:
√6 + 6 = √6 + √6²
This simplifies to:
√6 + √(6 · 6) = √6 + √(6²)
Since √(6²) = 6, the final simplified form is:
7√6
Therefore, the correct answer is B. 7√6.