Final Answer:
The final answer is 2√2 - √3. Therefore the correct answer is option a.
Step-by-step explanation:
To simplify the expression, start by expressing both terms as fourth roots of their respective numbers. The fourth root of 48 can be broken down as the fourth root of 16 times the fourth root of 3 (since 16 * 3 = 48). The fourth root of 16 is 2, and the fourth root of 3 remains as is. So, it becomes 2√3 - fourth root of 3. Simplifying further, it's 2√2 - √3, which matches option (a).
To break down the expression:
∜48 - ∜3 = ∜(16 * 3) - ∜3
∜48 - ∜3 = 2∜3 - ∜3
∜48 - ∜3 = 2√2 - √3
Therefore, the simplified form is 2√2 - √3.
This simplification involves recognizing the relationship between numbers and their fourth roots. By factoring 48 into its components, we simplify the expression to an easily recognizable form. The fourth root of 48 is reduced to 2 times the fourth root of 3, which when combined with the fourth root of 3, yields 2√2 - √3 as the final answer.
Understanding how to break down radicals and relate them to their numerical values helps simplify complex expressions, allowing for easier manipulation and calculation in mathematics. Therefore the correct answer is option a.