This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's simplify this expression. Step 1: Simplify the square roots in the numerator and denominator. sqrt(18) = sqrt(9 × 2) = 3sqrt(2) sqrt(50) = sqrt(25 × 2) = 5sqrt(2) Step 2: Substitute the simplified square roots back into the expression. 8 - 4sqrt(18)sqrt(50) = 8 - 4(3sqrt(2))5sqrt(2) = 8 - 12sqrt(2)5sqrt(2) Step 3: Rationalize the denominator by multiplying the numerator and denominator by sqrt(2). 8 - 12sqrt(2)5sqrt(2) × sqrt(2)sqrt(2) = (8 - 12sqrt(2))sqrt(2)5sqrt(2)sqrt(2) = 8sqrt(2) - 12(sqrt(2))^25(2) = 8sqrt(2) - 12(2)10 = 8sqrt(2) - 2410 Step 4: Separate the terms and simplify the fraction. = 8sqrt(2)10 - (24)/(10) = 4sqrt(2)5 - (12)/(5) Step 5: Rearrange the terms to match the form a + bsqrt(n). = -(12)/(5) + (4)/(5)sqrt(2) Step 6: Identify the values of a, b, and n. Comparing -(12)/(5) + (4)/(5)sqrt(2) with a + bsqrt(n): a = -(12)/(5) b = (4)/(5) n = 2 The simplified expression is -(12)/(5) + (4)/(5)sqrt(2). The values are a = -(12)/(5), b = (4)/(5), n = 2. 3 done, 2 left today. You're making progress.