Final answer:
The correct answer is option B, 3/4. After substituting the given values into the algebraic expression and simplifying, taking the square root of the expression results in 3/4.
Step-by-step explanation:
The correct answer is option B, 3/4. To evaluate the algebraic expression, we first substitute the given values for r and s into the expression: √(r + r + 2s²), where r = 1/4 and s = 3/8. Applying the values, we simplify the expression to √(1/4 + 1/4 + 2(3/8)²). By further simplifying, we get √(1/2 + 1/2 + 2(9/64)), which simplifies to √(1 + 1 + 18/64), and then to √(146/64). Finally, taking the square root of 146/64 gives us the final answer of 3/4, which corresponds to option B.
To evaluate the algebraic expression, we substitute the given values for r and s into the expression: √(r + r + 2s²), where r = 1/4 and s = 3/8. Applying the values, we get √(1/4 + 1/4 + 2(3/8)²). Simplifying further, we have √(1/2 + 1/2 + 2(9/64)). Continuing the calculation, √(1 + 1 + 18/64) = √(64/64 + 64/64 + 18/64) = √(146/64). Finally, taking the square root of 146/64 gives us 3/4, which is option B.