Solve the radical equation 400−6x3−−−−−−−−√5=4 .(1 point)
Responses
x=56−−√3
x equals root index 3 Start Root 56 End Root
x=−13−−√3
x equals negative root index 3 Start Root 13 End Root
x=−213−−√3
x equals negative 2 root index 3 Start Root 13 End Root
x=4
To solve this radical equation, we need to isolate the radical term and then square both sides of the equation to eliminate the square root.
Starting with the equation:
400 - √(6x^3) = 4
First, subtract 400 from both sides:
-√(6x^3) = -396
Next, square both sides of the equation to eliminate the square root:
(-√(6x^3))^2 = (-396)^2
6x^3 = 156816
Finally, divide both sides by 6 to solve for x^3:
x^3 = 26136
Take the cube root of both sides to solve for x:
x = ∛26136
So, the answer is x = ∛26136.