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.
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Here are the solutions to the problems: 10) What is the difference between the square of 4 (1)/(4) and the square root of 7 (9)/(16)? Step 1: Convert mixed numbers to improper fractions. 4 (1)/(4) = (4 × 4 + 1)/(4) = (17)/(4) 7 (9)/(16) = (7 × 16 + 9)/(16) = (112 + 9)/(16) = (121)/(16) Step 2: Calculate the square of 4 (1)/(4). ((17)/(4))^2 = (17^2)/(4^2) = (289)/(16) Step 3: Calculate the square root of 7 (9)/(16). sqrt((121)/(16)) = sqrt(121)sqrt(16) = (11)/(4) Step 4: Find the difference between the two values. (289)/(16) - (11)/(4) To subtract, find a common denominator, which is 16. (11)/(4) = (11 × 4)/(4 × 4) = (44)/(16) (289)/(16) - (44)/(16) = (289 - 44)/(16) = (245)/(16) Step 5: Convert the improper fraction to a mixed number. (245)/(16) = 15 (5)/(16) The difference is 15 (5)/(16). 11) Evaluate sqrt(0.000441) Step 1: Convert the decimal to a fraction. 0.000441 = (441)/(1000000) Step 2: Find the square root of the numerator and the denominator. sqrt(441) = 21 sqrt(1000000) = 1000 Step 3: Calculate the square root of the fraction. sqrt((441)/(1000000)) = (21)/(1000) Step 4: Convert the fraction back to a decimal. (21)/(1000) = 0.021 The value is 0.021. 12) Work out the square root of 0.2809 Step 1: Convert the decimal to a fraction. 0.2809 = (2809)/(10000) Step 2: Find the square root of the numerator and the denominator. sqrt(2809) = 53 sqrt(10000) = 100 Step 3: Calculate the square root of the fraction. sqrt((2809)/(10000)) = (53)/(100) Step 4: Convert the fraction ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._