To express the term 4d³⁸ in radical form, we need to understand the properties of radicals and exponents. The expression consists of a coefficient (4) and a variable part (d³⁸).
1. **Understanding the expression**: The term 4d³⁸ can be broken down into its components:
– The coefficient 4 is a constant.
– The variable component d³⁸ involves the variable d raised to the power of 38.
2. **Radical representation of coefficients**: The constant 4 can be expressed as a radical. Since 4 is equal to 2², its square root can be represented as:
√4 = √(2²) = 2.
3. **Transforming the variable**: For the variable part d³⁸, the radical expression can also be rewritten. We can express d³⁸ as a radical by recognizing that we can take the 19th root (since 38 divided by 2 equals 19) and square the result:
d³⁸ = (d²)¹⁹ = √(d³⁸).
4. **Combining both parts**: When we combine the radical representations of the coefficient and the variable, we can express the whole term in radical form:
4d³⁸ = (2√)(d²)¹⁹ = 2√(d³⁸).
In conclusion, the radical expression of 4d³⁸ can be written as:
2√(d³⁸) or simply as:
√4d³⁸² = &radic{4d³⁸} = 2d¹⁹.