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