![Evaluate without using tables or calculators: sqrt(0.8064 6.048 / 1.008 0.1344) and -4 of [(-4 + -5 / 15) + -3 - 4 / 6] / (84 / -7 + 3 - (-5)).](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1776498709654-8db7a6bc7d396fa4.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
Welcome back — missed you this week. Here are the solutions to your problems: 1. Evaluate without using tables or calculators. sqrt((0.8064 × 6.048)/(1.008 × 0.1344)) Step 1: Convert the decimals to integers by multiplying the numerator and denominator by appropriate powers of 10. sqrt((0.8064 × 6.048)/(1.008 × 0.1344)) = sqrt((8064 × 6048)/(1008 × 1344)) Step 2: Simplify the terms by division. Notice that 8064 ÷ 1008 = 8. sqrt((8 × 1008 × 6048)/(1008 × 1344)) = sqrt((8 × 6048)/(1344)) Now, simplify (6048)/(1344). (6048)/(1344) = (6048 ÷ 1344)/(1344 ÷ 1344) = 4.5 = (9)/(2) Step 3: Substitute the simplified fraction back into the square root. sqrt(8 × (9)/(2)) Step 4: Perform the multiplication and take the square root. sqrt((8 × 9)/(2)) = sqrt(4 × 9) = sqrt(36) = 6 The value is 6. 2. Evaluate; -4 of [(-4 + -5 ÷ 15) + -3 - 4 ÷ 6]84 ÷ -7 + 3 - (-5) Step 1: Evaluate the numerator. First, evaluate the expression inside the brackets: [(-4 + -5 ÷ 15) + -3 - 4 ÷ 6] Inside the first parenthesis: (-4 + -5 ÷ 15) -5 ÷ 15 = -(1)/(3) -4 + (-(1)/(3)) = -(12)/(3) - (1)/(3) = -(13)/(3) Now substitute this back into the brackets: [-(13)/(3) + -3 - 4 ÷ 6] Perform the division: 4 ÷ 6 = (4)/(6) = (2)/(3) The expression in brackets is: $[-(13)/(3) - 3 - 2