Question

HELP PLEASE!!!! Select all radical expressions that are equivalent to 5 2/3 . (5‾√3)2 (5‾√)3 52‾‾√ 10‾‾‾√3 52‾‾√3 15‾‾‾√

Answer 1

The radical expression equivalent to 5 2/3 is (5√3)² which represents the cube root of 5 squared, matching the fractional power of 5²/³.

Step-by-step explanation:

The question concerns the identification of radical expressions equivalent to the mixed number 5 2/3. When a number is expressed as a fractional power, such as x2 being equivalent to the square root of x (√x), it means that the number is raised to a fraction that indicates the root. Therefore, 52/3 represents the cube root of 5 squared.

• (5√3)2 means taking the cube root of 5 and then squaring it, which is equivalent to 52/3.
• 52√3 means squaring 5 and then taking the cube root, which is not equivalent to 52/3.
• 52√ means taking the square root of 5 squared, which is just 5.
• 10√3 is the cube root of 10, which is not equivalent to 52/3.
• 52√3, as aforementioned, is not equivalent to 52/3.
• 15√ means taking the square root of 15, which is not equivalent to 52/3.

Therefore, the radical expression equivalent to 5 2/3 is (5√3)2.