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
You're on a roll — To leave the answer in surd form, we need to rationalize the denominator. Step 1: Write the given expression. (1)/(sqrt(7)+2) Step 2: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of sqrt(7)+sqrt(2) is sqrt(7)-sqrt(2). (1)/(sqrt(7)+2) × sqrt(7)-sqrt(2)sqrt(7)-sqrt(2) Step 3: Perform the multiplication. Use the difference of squares formula (a+b)(a-b) = a^2 - b^2 for the denominator. 1 × (sqrt(7)-sqrt(2))(sqrt(7)+sqrt(2))(sqrt(7)-sqrt(2)) = sqrt(7)-sqrt(2)(sqrt(7))^2 - (sqrt(2))^2 Step 4: Simplify the denominator. sqrt(7)-sqrt(2)7 - 2 = sqrt(7)-sqrt(2)5 The simplified expression in surd form is sqrt(7)-sqrt(2)5. sqrt(7)-sqrt(2)5 Just one more to go today! Send it over.