![Evaluate the expression sqrt(2(1)/(4) x 1((1)/(3))2) + [3]3(3)/(8).](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1777130262570-e2a01a616e63c3f0.png&w=3840&q=75)
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
Step 1: Evaluate the first term of the expression. The first term is sqrt(2(1)/(4) × 1((1)/(3))^2). First, convert the mixed number to an improper fraction: 2(1)/(4) = ((2 × 4) + 1)/(4) = (8 + 1)/(4) = (9)/(4) Next, calculate the square of the fraction: ((1)/(3))^2 = (1^2)/(3^2) = (1)/(9) Now, substitute these values back into the first term: sqrt((9)/(4) × 1 × (1)/(9)) Multiply the fractions under the square root: sqrt((9)/(4) × (1)/(9)) = sqrt((9 × 1)/(4 × 9)) = sqrt((9)/(36)) Simplify the fraction: sqrt((9)/(36)) = sqrt((1)/(4)) Take the square root: sqrt((1)/(4)) = sqrt(1)sqrt(4) = (1)/(2) Step 2: Evaluate the second term of the expression. The second term is [3]3(3)/(8). First, convert the mixed number to an improper fraction: 3(3)/(8) = ((3 × 8) + 3)/(8) = (24 + 3)/(8) = (27)/(8) Now, take the cube root: 3/(8) = [3]27[3]8 Calculate the cube roots: [3]27 = 3 (since 3 × 3 × 3 = 27) [3]8 = 2 (since 2 × 2 × 2 = 8) So, the second term is: (3)/(2) Step 3: Add the results from Step 1 and Step 2. The total value of the expression is the sum of the two terms: (1)/(2) + (3)/(2) Add the fractions: (1+3)/(2) = (4)/(2) Simplify the result: (4)/(2) = 2 The value of the expression is 2. That's 2 down. 3 left today — send the next one.