what is the value of 3√1000?
The value of 3√1000 is approximately 15.59.
To find the value of 3√1000, we can use the fact that the cube root of a number is the number that, when multiplied by itself three times, gives the original number.
So, we need to find a number that, when multiplied by itself three times, equals 1000.
Let's start by finding the prime factorization of 1000:
1000 = 2 * 2 * 2 * 5 * 5 * 5
From this prime factorization, we can see that there is a 2 and a 5 present in the factorization. We need to find the highest perfect cube that can be formed using these prime factors.
The highest perfect cube formed by taking the factors three times is 2 * 2 * 2 = 8.
Now, we can rewrite 1000 as 8 * (2 * 5 * 5).
Taking the cube root of 8 gives us 2 because 2 * 2 * 2 = 8.
Thus, the value of 3√1000 is 2 * (2 * 5) = 2 * 10 = 20.