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 expression (1+sqrt(3))(1-sqrt(3)). This expression is in the form (a+b)(a-b), which simplifies to a^2 - b^2. Here, a=1 and b=sqrt(3). (1+sqrt(3))(1-sqrt(3)) = 1^2 - (sqrt(3))^2 = 1 - 3 = -2 The simplified expression is -2. Step 2: Evaluate (1)/(1+sqrt(3)) using the result from Step 1. To evaluate (1)/(1+sqrt(3)), we can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator, which is (1-sqrt(3)). (1)/(1+sqrt(3)) = (1)/(1+sqrt(3)) × 1-sqrt(3)1-sqrt(3) Using the result from Step 1, we know that (1+sqrt(3))(1-sqrt(3)) = -2. = 1-sqrt(3)-2 = -( sqrt(3)-1)-2 = sqrt(3)-12 Step 3: Substitute the given value of sqrt(3) = 1.7321. sqrt(3)-12 = (1.7321 - 1)/(2) = (0.7321)/(2) = 0.36605 Step 4: Round the result to 3 significant figures. The first three significant figures are 3, 6, and 6. The fourth digit is 0, so we do not round up. 0.36605 ≈ 0.366 The value of (1)/(1+sqrt(3)) to 3 significant figures is 0.366. That's 2 down. 3 left today — send the next one.