find the value of $sqrt3{-343}$.
find the value of $sqrt3{-343}$.
Answer
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 $y$ such that $y^3=-343$.
Step2: Factorize 343
We know that $343 = 7\times7\times7=7^3$. Since $(-7)\times(-7)\times(-7)=-343$ (because $(-a)\times(-a)\times(-a)=-a^3$ for any positive real number $a$).
Answer:
$-7$