Simplify the expression completely. -sqrt25+5sqrt(-25)-5root(3)(-125)+root(3)(-125) Answer:

Simplify -sqrt(25): First, let's simplify each term in the expression separately. -sqrt(25) simplifies to -5 because the square root of 25 is 5.Calculate 5sqrt(-25): Next, 5sqrt(-25) involves the square root of a negative number, which is not a real number. It is an imaginary number. The square root of -25 is 5i, where i is the imaginary unit. So, 5sqrt(-25) simplifies to 5 * 5i = 25i.Evaluate -5root(3)(-125): Then, -5root(3)(-125) simplifies to -5 * (-5) because the cube root of -125 is -5. So, -5root(3)(-125) simplifies to -5 * (-5) = 25.Find root(3)(-125): Finally, root(3)(-125) simplifies to -5 because the cube root of -125 is -5.Combine simplified terms: Now, we combine all the simplified terms: -5 + 25i + 25 - 5.Combine real numbers: Combining the real numbers: -5 + 25 - 5 = 15.Finalize imaginary term: The imaginary term remains as is because there are no other imaginary terms to combine it with.Final simplified expression: The final simplified expression is 15 + 25i.

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Simplify the expression completely.

-sqrt25+5sqrt(-25)-5root(3)(-125)+root(3)(-125)
Answer:

Simplify the expression completely. $\newline$ $-\sqrt{25}+5 \sqrt{-25}-5 \sqrt[3]{-125}+\sqrt[3]{-125}$ $\newline$ Answer:

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Algebra 2

Roots of rational numbers

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Q. Simplify the expression completely.

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-\sqrt{25}+5 \sqrt{-25}-5 \sqrt[3]{-125}+\sqrt[3]{-125}

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Answer:

Simplify $-\sqrt{25}$ : First, let's simplify each term in the expression separately. $-\sqrt{25}$ simplifies to $-5$ because the square root of $25$ is $5$ .
Calculate $5\sqrt{-25}$ : Next, $5\sqrt{-25}$ involves the square root of a negative number, which is not a real number. It is an imaginary number. The square root of $-25$ is $5i$ , where $i$ is the imaginary unit. So, $5\sqrt{-25}$ simplifies to $5 \times 5i = 25i$ .
Evaluate $-5\sqrt[3]{-125}$ : Then, $-5\sqrt[3]{-125}$ simplifies to $-5 \times (-5)$ because the cube root of $-125$ is $-5$ . So, $-5\sqrt[3]{-125}$ simplifies to $-5 \times (-5) = 25$ .
Find $\sqrt[3]{-125}$ : Finally, $\sqrt[3]{-125}$ simplifies to $-5$ because the cube root of $-125$ is $-5$ .
Combine simplified terms: Now, we combine all the simplified terms: $-5 + 25i + 25 - 5$ .
Combine real numbers: Combining the real numbers: $-5 + 25 - 5 = 15$ .
Finalize imaginary term: The imaginary term remains as is because there are no other imaginary terms to combine it with.
Final simplified expression: The final simplified expression is $15 + 25i$ .