This languages problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
You're on a roll — Step 1: Multiply the numerator and the denominator by the conjugate of the denominator. The given expression is 2+sqrt(3)2-sqrt(3). The conjugate of the denominator 2-sqrt(3) is 2+sqrt(3). Multiply the fraction by 2+sqrt(3)2+sqrt(3): 2+sqrt(3)2-sqrt(3) × 2+sqrt(3)2+sqrt(3) Step 2: Expand the numerator and the denominator. Numerator: (2+sqrt(3))(2+sqrt(3)) = (2)^2 + 2(2)(sqrt(3)) + (sqrt(3))^2 = 4 + 4sqrt(3) + 3 = 7 + 4sqrt(3) Denominator: (2-sqrt(3))(2+sqrt(3)). This is in the form (x-y)(x+y) = x^2 - y^2. So, (2)^2 - (sqrt(3))^2 = 4 - 3 = 1. Step 3: Simplify the expression. 7 + 4sqrt(3)1 = 7 + 4sqrt(3) The expression is in the form a + bsqrt(c), where a=7, b=4, and c=3. The rationalized expression is 7 + 4sqrt(3). What's next? 📸