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: Simplify the square roots in the expression. We have sqrt(100) = 10 and sqrt(169) = 13. Substitute these values into the given expression: 4sqrt(100)3sqrt(169) - sqrt(39) = (4 × 10)/(3 × 13 - sqrt(39)) Step 2: Perform the multiplications in the numerator and denominator. (40)/(39 - sqrt(39)) Step 3: Rationalize the denominator. To rationalize the denominator 39 - sqrt(39), multiply both the numerator and the denominator by its conjugate, which is 39 + sqrt(39). (40)/(39 - sqrt(39)) × 39 + sqrt(39)39 + sqrt(39) Step 4: Multiply the numerators and the denominators. For the numerator: 40(39 + sqrt(39)) For the denominator, use the difference of squares formula (a-b)(a+b) = a^2 - b^2: (39 - sqrt(39))(39 + sqrt(39)) = 39^2 - (sqrt(39))^2 Step 5: Calculate the values in the denominator. 39^2 = 1521 (sqrt(39))^2 = 39 So the denominator becomes: 1521 - 39 = 1482 Step 6: Write the expression with the rationalized denominator. 40(39 + sqrt(39))1482 Step 7: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor. Both 40 and 1482 are divisible by 2. 40 ÷ 2 = 20 1482 ÷ 2 = 741 The simplified expression is: 20(39 + sqrt(39))741 The final answer is 20(39 + sqrt(39))741. Send me the next one 📸