fourth root of (68-48sqrt2)
(68-48sqrt2)^(1/4) = (68-67.882)^(1/4) =
(0.118)^(1/4) = 0.5861
68-48√2 = 36-48√2+32 = (6-4√2)^2
6-4√2 = 4-4√2+2 = (2-√2)^2
So, ∜(68-48√2) = 2-√2 = .58578
To find the fourth root of the expression (68 - 48√2), we can follow these steps:
Step 1: Simplify the expression inside the fourth root:
(68 - 48√2)
= 68 - 48√2
Step 2: Apply the fourth root to the simplified expression:
∜(68 - 48√2)
Step 3: Express the expression in a simplified form, if possible:
We can start by factoring out the common factor of 4 from each term:
∜(4(17 - 12√2))
Next, we can simplify the expression under the fourth root further:
∜(4(17 - 12√2))
= ∜(4 * (2 * 8.5 - 2 * 6√2))
= ∜(4 * 2(8.5 - 6√2))
= ∜(8 * (8.5 - 6√2))
Step 4: Evaluate the fourth root expression using a calculator:
∜(8 * (8.5 - 6√2))
≈ ∜(54.400)
Using a calculator, we find that the fourth root of approximately 54.400 is equal to around 2.992.
Therefore, the fourth root of (68 - 48√2) is approximately 2.992.