Find all the real fourth roots of 256/2401
4/7 and 16/49
-4/7 and 4/7
4/7,-4/7, 16/49, - 16/49
4/7
To find the fourth roots of a number, we need to find all numbers that, when raised to the fourth power, equal the given number.
In this case, we are looking for all numbers that, when raised to the fourth power, equal 256/2401.
To find these numbers, we can set up the equation:
x^4 = 256/2401
Taking the fourth root of both sides, we find:
x = ± (256/2401)^(1/4)
Simplifying the right side, we have:
x = ± (2^8/7^4)^(1/4)
Using the property (a^m)^n = a^(m*n), we can simplify further:
x = ± 2^(8/4) / 7^(4/4)
x = ± 2^2 / 7^1
x = ± 4/7
Therefore, the real fourth roots of 256/2401 are 4/7 and -4/7.