Solve -343 = v^3, where v is a real number. Simplify your answer as much as possible.
Understand the Problem
The question requires us to solve the equation -343 = v^3 for the variable v, where v is a real number. We need to find the value of v and simplify our answer as much as possible.
Answer
$$ v = -7 $$
Answer for screen readers
The final answer is $$ v = -7 $$
Steps to Solve
-
Isolate the variable
To solve the equation $-343 = v^3$, we first want to isolate $v$. This can be done by multiplying both sides of the equation by -1:
$$343 = -v^3$$ -
Take the cube root
Next, we will take the cube root of both sides of the equation to solve for $v$:
$$ v = -\sqrt[3]{343} $$ -
Calculate the cube root
To find the value of $v$, we need to calculate $-\sqrt[3]{343}$:
We know that $343 = 7^3$, so:
$$ v = -\sqrt[3]{7^3} = -7 $$
The final answer is $$ v = -7 $$
More Information
The cube root of a number is the value that, when cubed, gives the original number. Since $343$ is a perfect cube ($7^3$), its cube root is easily calculated.
Tips
-
Forgetting the negative sign when isolating the variable on the left side of the equation.
- To avoid this, carefully track the signs when moving terms around in the equation.
-
Confusing cube roots with square roots.
- Remember that cube roots can yield one real solution, even if the original number is negative.
AI-generated content may contain errors. Please verify critical information
