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's the solution to question 3. a) Selesaikan (Solve) (i) Solve sqrt(13) × sqrt(13). Step 1: Multiply the square roots. When a square root is multiplied by itself, the result is the number inside the square root. sqrt(13) × sqrt(13) = sqrt(13 × 13) = sqrt(169) Step 2: Simplify the square root. sqrt(169) = 13 The solution is 13. (ii) Solve 3/(216) + 4^3. Step 1: Evaluate the cube root of the fraction. Find the cube root of the numerator and the denominator separately. [3]27 = 3 (since 3 × 3 × 3 = 27) [3]216 = 6 (since 6 × 6 × 6 = 216) So, 3/(216) = [3]27[3]216 = (3)/(6) Step 2: Simplify the fraction. (3)/(6) = (1)/(2) Step 3: Evaluate 4^3. 4^3 = 4 × 4 × 4 = 16 × 4 = 64 Step 4: Add the results from Step 2 and Step 3. (1)/(2) + 64 = 64(1)/(2) or 64.5 The solution is 64(1)/(2). b) Diberi (Given): -729 = a × a × a sqrt(49) = b + 2 Cari nilai a+b. (Find the value of a+b.) Step 1: Find the value of a. The equation is -729 = a × a × a, which can be written as a^3 = -729. To find a, take the cube root of -729. a = [3]-729 Since 9 × 9 × 9 = 729, then (-9) × (-9) × (-9) = -729. So, a = -9. Step 2: Find the value of b. The equation is sqrt(49) = b + 2. First, evaluate sqrt(49). sqrt(49) = 7 Substitute this value into the equation: 7 = b + 2 Subtract 2 from both sides to solve for b: b = 7 - 2 b = 5 Step 3: Find the value of a+b. Substitute the values of a and b found in Step 1 and Step 2. a+b = -9 + 5 a+b = -4 The value of a+b is -4. That's 2 down. 3 left today — send the next one.