Simplify the expression completely. -2sqrt(-49)-sqrt16+4root(3)(1000)-root(3)(216) Answer:

Simplify -2sqrt(-49): First, we will simplify each term in the expression separately. -2sqrt(-49) involves the square root of a negative number, which indicates the presence of an imaginary number.Simplify sqrt(16): The square root of -49 is 7i, where i is the imaginary unit. Therefore, -2sqrt(-49) becomes -2 * 7i, which simplifies to -14i.Simplify 4root(3)(1000): Next, we simplify sqrt(16). The square root of 16 is 4, so sqrt(16) simplifies to 4.Simplify root(3)(216): Now, we simplify 4root(3)(1000). The cube root of 1000 is 10, because 10^3 = 1000. Therefore, 4root(3)(1000) simplifies to 4 * 10, which is 40.Combine simplified terms: Finally, we simplify root(3)(216). The cube root of 216 is 6, because 6^3 = 216. Therefore, root(3)(216) simplifies to 6.Combine real numbers: Now we combine all the simplified terms: -14i - 4 + 40 - 6.Final simplified expression: Combining the real numbers gives us: 40 - 4 - 6, which simplifies to 30.The final simplified expression is 30 - 14i, which includes a real part and an imaginary part.

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Simplify the expression completely.

-2sqrt(-49)-sqrt16+4root(3)(1000)-root(3)(216)
Answer:

Simplify the expression completely. $\newline$ $-2 \sqrt{-49}-\sqrt{16}+4 \sqrt[3]{1000}-\sqrt[3]{216}$ $\newline$ Answer:

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Algebra 2

Roots of rational numbers

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Q. Simplify the expression completely.

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-2 \sqrt{-49}-\sqrt{16}+4 \sqrt[3]{1000}-\sqrt[3]{216}

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Answer:

Simplify $-2\sqrt{-49}$ : First, we will simplify each term in the expression separately. $-2\sqrt{-49}$ involves the square root of a negative number, which indicates the presence of an imaginary number.
Simplify $\sqrt{16}$ : The square root of $-49$ is $7i$ , where $i$ is the imaginary unit. Therefore, $-2\sqrt{-49}$ becomes $-2 \times 7i$ , which simplifies to $-14i$ .
Simplify $4\sqrt[3]{1000}$ : Next, we simplify $\sqrt{16}$ . The square root of $16$ is $4$ , so $\sqrt{16}$ simplifies to $4$ .
Simplify $\sqrt[3]{216}$ : Now, we simplify $4\sqrt[3]{1000}$ . The cube root of $1000$ is $10$ , because $10^3 = 1000$ . Therefore, $4\sqrt[3]{1000}$ simplifies to $4 \times 10$ , which is $40$ .
Combine simplified terms: Finally, we simplify $\sqrt[3]{216}$ . The cube root of $216$ is $6$ , because $6^3 = 216$ . Therefore, $\sqrt[3]{216}$ simplifies to $6$ .
Combine real numbers: Now we combine all the simplified terms: $-14i - 4 + 40 - 6$ .
Final simplified expression: Combining the real numbers gives us: $40 - 4 - 6$ , which simplifies to $30$ .
Final simplified expression: Combining the real numbers gives us: $40 - 4 - 6$ , which simplifies to $30$ .The final simplified expression is $30 - 14i$ , which includes a real part and an imaginary part.