# How do you simplify root3(1000)?

Apr 26, 2016

#### Answer:

$\sqrt[3]{1000} = 10$

#### Explanation:

Note that $1000 = 10 \times 10 \times 10 = {10}^{3}$

So: $\sqrt[3]{1000} = \sqrt[3]{{10}^{3}} = 10$

As a function from Real numbers to Real numbers, $f \left(x\right) = {x}^{3}$ is one-to-one with domain and range the whole of $\mathbb{R}$.

So the Real cube root ${f}^{- 1} \left(y\right) = \sqrt[3]{y}$ is also a well-defined one-to-one function with domain and range the whole of $\mathbb{R}$.

graph{(x^3 - y)(y^3-x) = 0 [-10, 10, -5, 5]}