Simplify the expression completely. -4sqrt(-100)-sqrt(-1)+root(3)(-125) Answer:

Rewrite square root: Simplify -4sqrt(-100). Since the square root of a negative number involves the imaginary unit i (where i^2 = -1), we can rewrite sqrt(-100) as sqrt(100) * sqrt(-1), which is 10i. Therefore, -4sqrt(-100) becomes -4 * 10i, which is -40i.Simplify negative square root: Simplify -sqrt(-1). The square root of -1 is the imaginary unit i, so -sqrt(-1) is simply -i.Find cube root: Simplify root(3)(-125). The cube root of -125 is -5 because (-5)^3 equals -125. So, root(3)(-125) is -5.Combine simplified terms: Combine the results from steps 1, 2, and 3. Now we add up the simplified terms: -40i - i - 5. Combining the like terms (the imaginary parts), we get -41i - 5.

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Simplify the expression completely.

-4sqrt(-100)-sqrt(-1)+root(3)(-125)
Answer:

Simplify the expression completely. $\newline$ $-4 \sqrt{-100}-\sqrt{-1}+\sqrt[3]{-125}$ $\newline$ Answer:

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Algebra 2

Roots of rational numbers

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Q. Simplify the expression completely.

\newline

-4 \sqrt{-100}-\sqrt{-1}+\sqrt[3]{-125}

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Answer:

Rewrite square root: Simplify $-4\sqrt{-100}$ . Since the square root of a negative number involves the imaginary unit $i$ (where $i^2 = -1$ ), we can rewrite $\sqrt{-100}$ as $\sqrt{100} \times \sqrt{-1}$ , which is $10i$ . Therefore, $-4\sqrt{-100}$ becomes $-4 \times 10i$ , which is $-40i$ .
Simplify negative square root: Simplify $-\sqrt{-1}$ . $\newline$ The square root of $-1$ is the imaginary unit $i$ , so $-\sqrt{-1}$ is simply $-i$ .
Find cube root: Simplify $\sqrt[3]{-125}$ . The cube root of $-125$ is $-5$ because $(-5)^3$ equals $-125$ . So, $\sqrt[3]{-125}$ is $-5$ .
Combine simplified terms: Combine the results from steps $1$ , $2$ , and $3$ . $\newline$ Now we add up the simplified terms: $-40i - i - 5$ . Combining the like terms (the imaginary parts), we get $-41i - 5$ .