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Simplify the expression completely.

root(3)(8)-sqrt(-9)-sqrt16-2root(3)(-125)
Answer:

Simplify the expression completely.\newline8391621253 \sqrt[3]{8}-\sqrt{-9}-\sqrt{16}-2 \sqrt[3]{-125} \newlineAnswer:

Full solution

Q. Simplify the expression completely.\newline8391621253 \sqrt[3]{8}-\sqrt{-9}-\sqrt{16}-2 \sqrt[3]{-125} \newlineAnswer:
  1. Simplify cube root of 88: We will start by simplifying each term in the expression separately.\newlineThe first term is 83\sqrt[3]{8}, which is the cube root of 88.\newlineTo find the cube root of 88, we look for a number that, when multiplied by itself three times, gives 88.\newline2×2×2=82 \times 2 \times 2 = 8, so 83=2\sqrt[3]{8} = 2.
  2. Square root of 9-9: The second term is 9\sqrt{-9}, which involves the square root of a negative number.\newlineThe square root of a negative number is not a real number; it is an imaginary number.\newline9\sqrt{-9} can be written as 9×1\sqrt{9} \times \sqrt{-1}, which equals 3i3i, where ii is the imaginary unit.
  3. Square root of 1616: The third term is 16\sqrt{16}, which is the square root of 1616.\newlineTo find the square root of 1616, we look for a number that, when squared, gives 1616.\newline4×4=164 \times 4 = 16, so 16=4\sqrt{16} = 4.
  4. Twice cube root of 125-125: The fourth term is 212532\sqrt[3]{-125}, which is twice the cube root of 125-125.\newlineTo find the cube root of 125-125, we look for a number that, when multiplied by itself three times, gives 125-125.\newline5×5×5=125-5 \times -5 \times -5 = -125, so 1253=5\sqrt[3]{-125} = -5.\newlineMultiplying this by 22 gives 21253=2×5=102\sqrt[3]{-125} = 2 \times -5 = -10.
  5. Combine simplified terms: Now we combine all the simplified terms:\newline8391621253\sqrt[3]{8} - \sqrt{-9} - \sqrt{16} - 2\sqrt[3]{-125}\newline= 23i4(10)2 - 3i - 4 - (-10)\newline= 23i4+102 - 3i - 4 + 10\newline= 2+1043i2 + 10 - 4 - 3i\newline= 83i8 - 3i.

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