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 tackle Question 3. QUESTION 3 3.1.1 Rationalise the denominator of (4)/(3sqrt(5)). Step 1: Multiply the numerator and denominator by sqrt(5) to eliminate the radical in the denominator. (4)/(3sqrt(5)) × sqrt(5)sqrt(5) Step 2: Perform the multiplication. 4sqrt(5)3 × (sqrt(5) × sqrt(5)) = 4sqrt(5)3 × 5 = 4sqrt(5)15 The rationalized expression is 4sqrt(5)15. 3.1.2 Rationalise the denominator of (2)/(sqrt(6)-2). Step 1: Multiply the numerator and denominator by the conjugate of the denominator, which is sqrt(6)+2. (2)/(sqrt(6)-2) × sqrt(6)+2sqrt(6)+2 Step 2: Multiply the numerators and denominators. Remember that (sqrt(a)-b)(sqrt(a)+b) = (sqrt(a))^2 - b^2. 2(sqrt(6)+2)(sqrt(6))^2 - (2)^2 Step 3: Simplify the expression. 2sqrt(6) + 2 × 26 - 4 = 2sqrt(6) + 42 Step 4: Divide both terms in the numerator by the denominator. 2sqrt(6)2 + (4)/(2) = sqrt(6) + 2 The rationalized expression is sqrt(6)+2. What's next?