Answer:
1/2
Step-by-step explanation:
Absolute value symbols are only needed in certain cases when finding the nth root of a number when n is even. For example, the 4th root of (-2) ^ 20 is |(-2) ^ 5| or 32. To find a cube root, work backwards. Find a number whose cube is the radicand.
Notice that the radical expression is of the form n√b, where b is a real number and n is a positive integer. This expression can be written as an exponential equation of the form a^n = b, where a is also a real number.
Write 3 √216/1728 as an exponential equation of the form a^n = b
a^3 = 216/1728
Because n is odd, there is only one value of a that makes the equation true. In this case, a will be a fraction. Determine the numerator of a. Find the number that, when cubed, is 216.
(6)^3 = 216
Now determine the denominator of a. Find the number that, when cubed, is 1728.
(12)^3 = 1728
Use the numerator and denominator found above to complete the equation a^3 = 216/1728. . Since n is odd, absolute value symbols are not necessary.
(6/12)^3 = 216/1728
Finally, simplify this value of a.
6/12 = 1/2
Therefore, 3 √216/1728 = 1/2
