Question

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

Answer 1

Answer:

Square is number which we get after multiply a number x to itself where as cube is a number which we get after multiplying a number x to itself three times.

Given number is 64

To find the square root or cube root of any number just right it using prime factorization method .

Then 64 can be written as 64=2×2×2×2×2×2

For square root we form two pairs of exactly same factors as 64=2×2×2×2×2×2 = 8×8

∴ Square root of 64 =8

For cube root we form three pairs of exactly same factors as 64=2×2×2×2×2×2=4×4×4

∴ Cube root of 64 =4.

Answer 2

In order to find the square root, we must find a number that when multiplied by itself one time, it produces the number under consideration.
In the case of 64, the square root is 8 because 8 multiplied once by itself is 64.

However, when finding the cube root, the root must multiply by itself two times and make the number. 
In the case of 64, 4 multiplied by itself two times is 64.