Simplify the expression completely. -root(3)(729)-3sqrt36+sqrt(-100)+3root(3)(125) Answer:

Cube Root of 729: First, we will simplify each term in the expression separately, starting with the cube root of 729. -root(3)(729) = -root(3)(9*9*9) = -root(3)(9^3) = -9Square Root of 36: Next, we simplify the square root of 36. -3sqrt(36) = -3*6 = -18Square Root of -100: Now, we simplify the square root of -100. Since the square root of a negative number is not a real number, we will express it in terms of i, where i is the imaginary unit. sqrt(-100) = sqrt(100) * sqrt(-1) = 10iCube Root of 125: Finally, we simplify the cube root of 125. 3root(3)(125) = 3root(3)(5*5*5) = 3root(3)(5^3) = 3*5 = 15Combine Simplified Terms: Now we combine all the simplified terms to get the final answer. Answer = -9 - 18 + 10i + 15 = -12 + 10i

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Simplify the expression completely.

-root(3)(729)-3sqrt36+sqrt(-100)+3root(3)(125)
Answer:

Simplify the expression completely. $\newline$ $-\sqrt[3]{729}-3 \sqrt{36}+\sqrt{-100}+3 \sqrt[3]{125}$ $\newline$ Answer:

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Algebra 2

Roots of rational numbers

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Q. Simplify the expression completely.

\newline

-\sqrt[3]{729}-3 \sqrt{36}+\sqrt{-100}+3 \sqrt[3]{125}

\newline

Answer:

Cube Root of $729$ : First, we will simplify each term in the expression separately, starting with the cube root of $729$ . $\newline$ -\sqrt[\(3]{ $729$ } = -\sqrt[ $3$ ]{ $9$ \times $9$ \times $9$ } = -\sqrt[ $3$ ]{ $9$ ^ $3$ } = $-9$
Square Root of $36$ : Next, we simplify the square root of $36$ . $\newline$ $-3\sqrt{36} = -3\times 6 = -18$
Square Root of $-100$ : Now, we simplify the square root of $-100$ . Since the square root of a negative number is not a real number, we will express it in terms of $i$ , where $i$ is the imaginary unit. $\newline$ $\sqrt{-100} = \sqrt{100} \times \sqrt{-1} = 10i$
Cube Root of $125$ : Finally, we simplify the cube root of $125$ . $\sqrt[3]{125} = \sqrt[3]{5\times5\times5} = \sqrt[3]{5^3} = 3\times5 = 15$
Combine Simplified Terms: Now we combine all the simplified terms to get the final answer. $\newline$ Answer = $-9 - 18 + 10i + 15 = -12 + 10i$