Question

what is the value of $sqrt3{1,000}$? type the number in the box.

Explanation:

Step1: Recall cube - root definition

The cube - root of a number $x$, denoted as $\sqrt[3]{x}$, is a number $y$ such that $y^3=x$. We need to find a number $y$ where $y^3 = 1000$.

Step2: Factorize 1000

We know that $1000=10\times10\times10 = 10^3$. So, $\sqrt[3]{1000}=\sqrt[3]{10^3}$.

Step3: Simplify the cube - root

According to the property $\sqrt[3]{a^3}=a$ for any real number $a$, when $a = 10$, $\sqrt[3]{10^3}=10$.

Answer:

10