Final answer:
The value of n is 4√(2).
Step-by-step explanation:
To find the value of n, we can start by simplifying the equation (2x)³ = √(128). Taking the cube root of both sides gives us 2x = √(2³ × 4²). Simplifying the right side gives us 2x = 2² × 4 = 16. Dividing both sides by 2 gives us x = 8.
We are given that x = n√(2), so substituting the value of x into the equation gives us 8 = n√(2). To solve for n, we need to isolate it on one side of the equation. Dividing both sides by √(2), we get n = 8/√(2). Rationalizing the denominator by multiplying both the numerator and denominator by √(2), we get n = 8√(2)/2 = 4√(2).