Q. Simplify the expression completely.−53−1+5−100+36+3343Answer:
Identify Terms: Identify the terms in the expression and simplify each term separately.−53−1 involves the cube root of −1.5−100 involves the square root of −100, which is a complex number since the square root of a negative number is not real.36 involves the square root of 36.3343 involves the cube root of 343.
Simplify −53−1: Simplify −53−1. The cube root of −1 is −1, so −5 times the cube root of −1 is −5 times −1, which equals 5.
Simplify 5−100: Simplify 5−100. The square root of −100 is not a real number; it is 10i, where i is the imaginary unit. So, 5 times the square root of −100 is 5 times 10i, which equals 50i.
Simplify 36: Simplify 36.The square root of 36 is 6, since 6 times 6 equals 36.
Simplify 3343: Simplify 3343. The cube root of 343 is 7, since 7×7×7 equals 343.
Combine Simplified Terms: Combine the simplified terms.Add the real number terms 5 and 6, and keep the imaginary term 50i separate. The cube root of 343, which is 7, is also a real number and can be added to the other real numbers.5+6+7=18
Write Final Expression: Write the final simplified expression.The real part is 18, and the imaginary part is 50i. Since the original problem did not specify that we should only find the real-number root, we include the imaginary part in our answer.The final simplified expression is 18+50i.