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 root inside the parentheses. sqrt(4) = 2 Substitute this value back into the expression: 2((2)/(6) ÷ 2sqrt(3)5) Step 2: Simplify the fraction (2)/(6) inside the parentheses. (2)/(6) = (1)/(3) The expression becomes: 2((1)/(3) ÷ 2sqrt(3)5) Step 3: Perform the division inside the parentheses. To divide by a fraction, multiply by its reciprocal. (1)/(3) ÷ 2sqrt(3)5 = (1)/(3) × (5)/(2sqrt(3)) = (5)/(6sqrt(3)) The expression is now: 2((5)/(6sqrt(3))) Step 4: Multiply the result by 2. 2 × (5)/(6sqrt(3)) = (10)/(6sqrt(3)) Step 5: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2. (10)/(6sqrt(3)) = (5)/(3sqrt(3)) Step 6: Rationalize the denominator by multiplying the numerator and denominator by sqrt(3). (5)/(3sqrt(3)) × sqrt(3)sqrt(3) = 5sqrt(3)3 × (sqrt(3))^2 = 5sqrt(3)3 × 3 = 5sqrt(3)9 The simplified expression is 5sqrt(3)9. That's 2 down. 3 left today — send the next one.