Final answer:
To find the rational approximation of √15, we can use the method of continued fractions. By expressing the square root as a fraction and simplifying it using the conjugate, we can find a rational approximation.
Step-by-step explanation:
To find the rational approximation of √15, we can use the method of continued fractions. We start by expressing the square root as a fraction: √15 = 3 + 1/(√15 - 3). We can simplify this further by multiplying the numerator and denominator by the conjugate of the denominator: √15 = 3 + 1/(2 + √15 - 3). Now, we can simplify the expression by adding the fractions, resulting in √15 = 3 + 1/(2 + 12 - 3).