Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$-11 \sqrt[5]{D}-11=44$
Answer (1)
Add 11 to both sides: − 11 5 D = 55 .
Divide both sides by -11: 5 D = − 5 .
Raise both sides to the power of 5: D = ( − 5 ) 5 .
Calculate the result: − 3125 .
Explanation
Problem Analysis We are given the equation − 11 5 D − 11 = 44 and we want to solve for D .
Isolating the Root Term First, we isolate the term with the fifth root of D by adding 11 to both sides of the equation: − 11 5 D − 11 + 11 = 44 + 11
− 11 5 D = 55
Isolating the Fifth Root Next, we divide both sides by -11 to isolate the fifth root: − 11 − 11 5 D = − 11 55
5 D = − 5
Eliminating the Fifth Root Now, we raise both sides to the power of 5 to eliminate the fifth root: ( 5 D ) 5 = ( − 5 ) 5
D = ( − 5 ) 5
Calculating the Value of D Finally, we calculate ( − 5 ) 5 : D = − 3125
Final Answer Since the problem asks us to round to two decimal places if necessary, and our answer is an integer, we don't need to round.
Examples
Understanding equations with radicals is crucial in many fields, such as physics and engineering. For instance, when calculating the period of a pendulum, you encounter a square root. Similarly, in electrical engineering, determining the impedance of a circuit involves square roots. By mastering these equations, you can solve real-world problems related to oscillations, wave phenomena, and circuit analysis.
