Final answer:
The correct option is option a (3d = √(d+5)), which features a variable inside a radical, thereby classifying it as a radical equation. To solve this equation, isolate the radical, square both sides, and then solve the resulting quadratic equation.
Step-by-step explanation:
The question asks which of the options is a radical equation. A radical equation is one that includes a variable inside a radical, such as a square root. Upon reviewing the options given:
- a. 3d = √(d+5) is a radical equation because it has the variable 'd' inside the square root.
- b. ³√8 + 2n = ³√12 + n is not a pure radical equation because the variable 'n' is not inside the cube root.
- c. √10 + h = 5 + 2h is not a radical equation because the variable 'h' is not inside the square root.
- d. ³√8 + d² = d√16 is not a radical equation because 'd' is not inside a radical; it is either squared or multiplied by a radical containing a constant
Hence, the correct option is option a, which is the radical equation 3d = √(d+5).
To solve this mathematical problem completely, you need to isolate the radical on one side of the equation and then square both sides to eliminate the radical:
- Begin with the equation: 3d = √(d+5).
- Isolate the radical: √(d+5) = 3d.
- Square both sides: (√(d+5))² = (3d)².
- Simplify: d + 5 = 9d².
- Rearrange the equation: 9d² - d - 5 = 0.
- Now, this is a quadratic equation which can be solved using the quadratic formula or factoring, depending on the nature of its solutions.