Q. Simplify the expression completely.38−−9−16−23−125Answer:
Simplify cube root of 8: We will start by simplifying each term in the expression separately.The first term is 38, which is the cube root of 8.To find the cube root of 8, we look for a number that, when multiplied by itself three times, gives 8.2×2×2=8, so 38=2.
Square root of −9: The second term is −9, which involves the square root of a negative number.The square root of a negative number is not a real number; it is an imaginary number.−9 can be written as 9×−1, which equals 3i, where i is the imaginary unit.
Square root of 16: The third term is 16, which is the square root of 16.To find the square root of 16, we look for a number that, when squared, gives 16.4×4=16, so 16=4.
Twice cube root of −125: The fourth term is 23−125, which is twice the cube root of −125.To find the cube root of −125, we look for a number that, when multiplied by itself three times, gives −125.−5×−5×−5=−125, so 3−125=−5.Multiplying this by 2 gives 23−125=2×−5=−10.
Combine simplified terms: Now we combine all the simplified terms:38−−9−16−23−125= 2−3i−4−(−10)= 2−3i−4+10= 2+10−4−3i= 8−3i.