3√47

To simplify the cube root of 47, we can use prime factorization.

First, let's find the prime factors of 47:

47 is a prime number, as it cannot be divided evenly by any other number except 1 and itself.

Now, let's group the prime factors in sets of three:

47 = 47^1 = (2^3)(5^0)(3^0)

We can simplify the expression by taking one factor from each group of three:

3√47 = 3√[(2^3)(5^0)(3^0)]

Since there is only one factor in each group of three, the simplified expression is:

3√(47)