Final answer:
To simplify the expression √(3√6), rewrite it as (√3) * (√√6). By applying the rule of exponents, (√3) * (√√6) simplifies to √3 * √(6^(1/4)). Therefore, the answer is Option 1: √3√2.
Step-by-step explanation:
To simplify the expression √(3√6), we can rewrite it as (√3) * (√√6). Now, √3 is equivalent to the square root of 3, and √√6 is equivalent to the square root of the square root of 6. To calculate the square root of a number, we can raise that number to the power of 1/2. So, (√3) * (√√6) becomes (3^(1/2)) * ((6^(1/2))^(1/2)).
By applying the rule of exponents, we can simplify the expression further. (3^(1/2)) * ((6^(1/2))^(1/2)) becomes (3^(1/2)) * ((6^(1/4))). Now, raising 3 to the power of 1/2 is equivalent to taking the square root of 3, which simplifies to √3.
Therefore, √(3√6) is equal to √3 * √(6^(1/4)). And simplifying √(6^(1/4)) gives us √(√6), which is equivalent to (√√6). So, the answer is √3 * (√√6), which is Option 1: √3√2.