Question

how does finding the square root of a square root of a number compare to finding the cube root of a number? use the number 64 in your explanation.

Answer 1

Finding the square root of a square root of a number (e.g., √√64) gives a different result than finding the cube root of a number (e.g., ∛64), with the former being a successive application of the square root operation and the latter involving finding a single number that when cubed equals the original number.

Step-by-step explanation:

Finding the square root of a square root of a number and finding the cube root of a number involve different procedures and result in different values. For example, let's use the number 64. The square root of 64 is 8, because 8 squared (8²) is 64. To find the square root of the square root, we take the square root of 8, which is 2 since 2 squared (2²) is 4, and 4 squared (4²) is 16. In contrast, the cube root of 64 is 4, because 4 cubed (4³) is 64. These roots represent different levels of the same operation, and each sequence comes with separate rules and outcomes.

Using a calculator to perform these operations can greatly simplify the process. For example, you can simply type in the square root function, and then apply it again to get the square root of a square root. Equally, you can enter the cube root function directly or raise the number to the power of 1/3 to obtain the cube root.

Answer 2

Instead of finding a number multiplied by itself twice, you look for a number multiplied by itself three times. For example, 4 is the square root of 16 because 4*4=16. 4 is the cube root of 64 because 4*4*4=64