Algebra 2
Radicals and Rational Exponents flashcards
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- In Nth Roots and Rational Exponents, what does principal even roots mean?Nth Roots and Rational Exponents
- The defined nonnegative output of an even root in the reals.
- Is √(x²) always x?Nth Roots and Rational Exponents
- No, it is |x| for real x.
- In Nth Roots and Rational Exponents, what does odd roots mean?Nth Roots and Rational Exponents
- A real nth root for an odd index.
- Why can ∛(−8) equal −2?Nth Roots and Rational Exponents
- Because (−2)³=−8.
- In Nth Roots and Rational Exponents, what does rational exponents mean?Nth Roots and Rational Exponents
- A fractional-power notation for roots and powers.
- Why state the real domain?Nth Roots and Rational Exponents
- An even root of a negative base is not real.
- In Simplifying Radical Expressions, what does perfect-power factors mean?Simplifying Radical Expressions
- Removing known perfect powers from a root.
- Why is √(x²)=|x|?Simplifying Radical Expressions
- A principal square root cannot be negative.
- In Simplifying Radical Expressions, what does product rule conditions mean?Simplifying Radical Expressions
- A root-product rule under valid real assumptions.
- Can √(a+b) usually split into √a+√b?Simplifying Radical Expressions
- No, roots do not distribute across addition.
- In Simplifying Radical Expressions, what does equivalent forms mean?Simplifying Radical Expressions
- An alternate notation with the same value on a shared domain.
- Why check domains after rewriting?Simplifying Radical Expressions
- An algebraic rewrite may appear to accept an invalid input.
- In Radical Operations, what does like radical addition mean?Radical Operations
- Adding coefficients of matching radical terms.
- Can √2 and √3 combine as 2√5?Radical Operations
- No, their radicands differ.
- In Radical Operations, what does multiplying radicals mean?Radical Operations
- A product of radical expressions.
- Why simplify after multiplication?Radical Operations
- The new radicand may contain extractable perfect powers.
- In Radical Operations, what does division and restrictions mean?Radical Operations
- An equivalent quotient with domain safeguards.
- Why state a denominator restriction?Radical Operations
- Zero in any denominator makes the original expression undefined.
- In Radical Functions and Inverses, what does square-root graph mean?Radical Functions and Inverses
- A translated principal square-root function.
- What is its least real input?Radical Functions and Inverses
- The horizontal shift h.
- In Radical Functions and Inverses, what does cube-root graph mean?Radical Functions and Inverses
- The real odd-root family across every real x.
- Why can negative inputs work?Radical Functions and Inverses
- Odd powers of negative numbers are negative.
- In Radical Functions and Inverses, what does inverse pair mean?Radical Functions and Inverses
- Two functions with reversed allowed input-output pairs.
- Why restrict x² to x≥0?Radical Functions and Inverses
- Without it, different inputs give the same output.
- In Radical Equations, what does isolate before squaring mean?Radical Equations
- A staged method for a radical equation.
- Why isolate the radical first?Radical Equations
- Squaring a sum creates cross terms.
- In Radical Equations, what does extraneous solutions mean?Radical Equations
- A candidate introduced by a nonreversible step.
- Where should candidates be checked?Radical Equations
- In the unsquared original equation.
- In Radical Equations, what does real-domain checks mean?Radical Equations
- The allowable inputs and outputs of a real radical equation.
- Can √x equal a negative real number?Radical Equations
- No, its principal value is nonnegative.