Simplify
^3sqrt1000
To simplify the expression ^3√1000, we need to find the cube root of 1000.
One way to find the cube root is to prime factorize the number.
Let's prime factorize 1000:
1000 = 2 * 2 * 2 * 5 * 5 * 5
Now, we group the prime factors in groups of three:
1000 = 2 * (2 * 2) * (5 * 5) * 5
Taking one factor from each group, we can rewrite 1000 as:
1000 = 2^3 * 5^2
Now, we can rewrite the expression ^3√1000 as:
^3√(2^3 * 5^2)
Simplifying, we get:
^3√(2^3) * ^3√(5^2)
And further simplifying:
2 * 5
Finally, we get:
^3√1000 = 10