Question

Which of the following expressions are equivalent to 4√3?

a) 4¹/⁸ + 3¹/⁸
b) 27¹/² + 3¹/²
c) √32
d) √48

Answer 1

The expression equivalent to 4√3 is √48. On simplifying √48, we find it equals 4√3 since √48 can be factored into √(16×3) which further simplifies to 4√3.

Step-by-step explanation:

The student's question asks which of the given expressions is equivalent to 4√3. The correct answer is √48. To simplify √48, we can factor it as √(16×3), which simplifies to √16 * √3. Since √16 is equal to 4, we have 4√3.

For clarity:

• a) 4¹/⁸ + 3¹/⁸ is not equivalent because it represents the sum of two different radicals.
• b) 27¹/² + 3¹/² simplifies to 3√3 + √3, which is also not equivalent.
• c) √32 can be written as 4√2, which is not equivalent to 4√3.
• d) √48 is equivalent, as explained above.