Simplify the expression completely. 3root(3)(-8)-5sqrt(-49)-root(3)(-216) Answer:

Cube Root of -8: Simplify the cube root of -8. The cube root of -8 is -2 because (-2)^3 = -8. 3 * cube root of -8 = 3 * (-2) = -6Square Root of -49: Simplify the square root of -49. The square root of a negative number involves an imaginary unit i, where i^2 = -1. Square root of -49 = sqrt(49) * sqrt(-1) = 7i 5 * sqrt(-49) = 5 * 7i = 35iCube Root of -216: Simplify the cube root of -216. The cube root of -216 is -6 because (-6)^3 = -216. Cube root of -216 = -6Combine Results: Combine the results from steps 1, 2, and 3. The expression now becomes -6 - 35i - 6. Combine the real numbers: -6 - 6 = -12 The imaginary part remains unchanged: - 35i The simplified expression is -12 - 35i.

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Simplify the expression completely.

3root(3)(-8)-5sqrt(-49)-root(3)(-216)
Answer:

Simplify the expression completely. $\newline$ $3 \sqrt[3]{-8}-5 \sqrt{-49}-\sqrt[3]{-216}$ $\newline$ Answer:

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Algebra 2

Roots of rational numbers

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Q. Simplify the expression completely.

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3 \sqrt[3]{-8}-5 \sqrt{-49}-\sqrt[3]{-216}

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Answer:

Cube Root of $-8$ : Simplify the cube root of $-8$ . The cube root of $-8$ is $-2$ because $(-2)^3 = -8$ . $3 \times$ cube root of $-8$ = $3 \times (-2) = -6$
Square Root of $-49$ : Simplify the square root of \(-49＂). $\newline$ The square root of a negative number involves an imaginary unit i＂), where \(i^\(2 = $-1$ ＂). $\newline$ Square root of \(-49 = \sqrt{ $49$ } \times \sqrt{ $-1$ } = $7$ i＂). $\newline$ \(5 \times \sqrt{ $-49$ } = $5$ \times $7$ i = $35$ i＂)
Cube Root of $-216$ : Simplify the cube root of $-216$ . The cube root of $-216$ is $-6$ because $(-6)^3 = -216$ . Cube root of $-216$ = $-6$
Combine Results: Combine the results from steps $1$ , $2$ , and $3$ . $\newline$ The expression now becomes $-6 - 35i - 6$ . $\newline$ Combine the real numbers: $-6 - 6 = -12$ $\newline$ The imaginary part remains unchanged: $- 35i$ $\newline$ The simplified expression is $-12 - 35i$ .