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Simplify the expression completely.

-5root(3)(-1)+5sqrt(-100)+sqrt36+root(3)(343)
Answer:

Simplify the expression completely.\newline513+5100+36+3433 -5 \sqrt[3]{-1}+5 \sqrt{-100}+\sqrt{36}+\sqrt[3]{343} \newlineAnswer:

Full solution

Q. Simplify the expression completely.\newline513+5100+36+3433 -5 \sqrt[3]{-1}+5 \sqrt{-100}+\sqrt{36}+\sqrt[3]{343} \newlineAnswer:
  1. Identify Terms: Identify the terms in the expression and simplify each term separately.\newline513-5\sqrt[3]{-1} involves the cube root of 1-1.\newline51005\sqrt{-100} involves the square root of 100-100, which is a complex number since the square root of a negative number is not real.\newline36\sqrt{36} involves the square root of 3636.\newline3433\sqrt[3]{343} involves the cube root of 343343.
  2. Simplify 513-5\sqrt[3]{-1}: Simplify 513-5\sqrt[3]{-1}. The cube root of 1-1 is 1-1, so 5-5 times the cube root of 1-1 is 5-5 times 1-1, which equals 55.
  3. Simplify 51005\sqrt{-100}: Simplify 51005\sqrt{-100}. The square root of 100-100 is not a real number; it is 10i10i, where ii is the imaginary unit. So, 55 times the square root of 100-100 is 55 times 10i10i, which equals 50i50i.
  4. Simplify 36\sqrt{36}: Simplify 36\sqrt{36}.\newlineThe square root of 3636 is 66, since 66 times 66 equals 3636.
  5. Simplify 3433\sqrt[3]{343}: Simplify 3433\sqrt[3]{343}. The cube root of 343343 is 77, since 7×7×77 \times 7 \times 7 equals 343343.
  6. Combine Simplified Terms: Combine the simplified terms.\newlineAdd the real number terms 55 and 66, and keep the imaginary term 50i50i separate. The cube root of 343343, which is 77, is also a real number and can be added to the other real numbers.\newline5+6+7=185 + 6 + 7 = 18
  7. Write Final Expression: Write the final simplified expression.\newlineThe real part is 1818, and the imaginary part is 50i50i. Since the original problem did not specify that we should only find the real-number root, we include the imaginary part in our answer.\newlineThe final simplified expression is 18+50i18 + 50i.

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