Question

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

Answer 1

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.