Questions and Answers
Evaluate the radical expression: √1/16
1/4
Evaluate the radical expression: √145
12.04
Evaluate the radical expression: −√64
-8
Simplify √32
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Simplify √25x^8
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Simplify √9x^10
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Simplify (16/25)^1/2
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Multiply and simplify the radical expressions: (√7 + 3)(√7 + 6)
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Solve the following radical equation: 1 = √−7 − 2z
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Solve the following radical equation: √4 − z = −5
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Study Notes
Radical Expressions and Their Evaluations
- ( \sqrt{\frac{1}{16}} = \frac{1}{4} )
- ( \sqrt{145} \approx 12.04 )
- ( -\sqrt{64} = -8 )
Simplifying Radical Expressions
- ( \sqrt{32} ) simplifies to ( 4\sqrt{2} )
- ( \sqrt{25x^8} ) simplifies to ( 5x^4 )
- ( \sqrt{9x^{10}} ) simplifies to ( 3x^5 )
- ( \left(\frac{16}{25}\right)^{\frac{1}{2}} = \frac{4}{5} )
Operations with Radical Expressions
- Multiply and simplify:
- ( (\sqrt{7} + 3)(\sqrt{7} + 6) = 25 + 9\sqrt{7} )
Solving Radical Equations
- For ( 1 = \sqrt{-7} - 2z ), the solution is ( z = -4 )
- The equation ( \sqrt{4} - z = -5 ) has no solution, indicating a contradiction.
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Description
This quiz covers the evaluation, simplification, and operations involving radical expressions, along with solving radical equations. Test your knowledge on key concepts such as simplification and the properties of radicals to enhance your algebra skills.
