The discussion focuses on simplifying radical expressions, specifically the expression 8^(3/2) and its equivalent forms. Participants clarify that the expression can be rewritten as (81/2)^3 and simplified to 16√2. The conversation emphasizes the importance of knowing when to present answers in square root form versus exponential form, with a preference for retaining square roots in final answers unless a decimal approximation is more practical. The consensus is that simplification should continue until reaching a prime number.
PREREQUISITESStudents, educators, and professionals in mathematics or engineering who seek to enhance their understanding of simplifying radical expressions and the appropriate contexts for different forms of answers.
CSmith said:1.) 8 3/2
=(81/2)3
=(2 squareroot 8)2
(2 square root 2x2x2)3
=(2 square root )3
=2 square root x 2 square root x 2 square root=8 (2 square root)
=16 square root 2
CSmith said:how do i know when the answer should be in square root form like 16 square root 2 or when it is suppose to be in powers like my answer for 32 2/5 when the answer was 2^2.
Jameson said:The final answer to that problem is 4. There's no reason to write it as 2^2.
With square roots, you simplify as much as you can until you are left with a prime number, so you must keep the square root sign or use a decimal approximation, which is not preferred. If you have something like [math]\sqrt{20}[/math] then you can simplify it but there will be a square root in the final answer.