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Questions and Answers
Find all the real square roots of -9/16.
Find all the real square roots of -9/16.
no real root
Find all the real cube roots of -0.000125.
Find all the real cube roots of -0.000125.
-0.05
What is a simpler form of the radical expression √36g⁶?
What is a simpler form of the radical expression √36g⁶?
6|g³|
What is a simpler form of the radical expression ³√125x²¹y²⁴?
What is a simpler form of the radical expression ³√125x²¹y²⁴?
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Which of the following is a simpler form of the radical expression √27x⁴/75y²?
Which of the following is a simpler form of the radical expression √27x⁴/75y²?
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Study Notes
Square Roots of Negative Numbers
- Real square roots of negative numbers do not exist; thus, -9/16 has no real roots.
Cube Roots of Negative Numbers
- The cube root of a negative number is negative; the real cube root of -0.000125 is -0.05.
Simplifying Radical Expressions
- The expression √36g⁶ simplifies to 6|g³|, indicating how to handle square roots with variables.
Higher-Order Radical Expressions
- The expression ³√125x²¹y²⁴ simplifies to 5x⁷y⁸, demonstrating the simplification process for cube roots.
Simplifying Fractions with Radicals
- For the expression √27x⁴/75y², the simpler form is 3x²/5|y|, showing how to reduce radicals in fractional expressions.
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