Card 1 of 20
EasyStudy card 1
Prompt
In \(\sqrt[n]{a}\), what is \(n\)?
Answer
The index.
MathChapter 13: Polynomial and Radical Functions
Flashcards
Radical Expressions Flashcards
Twenty focused cards on radical anatomy, rational exponents, simplification, operations, and rationalization.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
In \(\sqrt[n]{a}\), what is \(a\)?
Answer
The radicand.
Card 3 of 20
EasyStudy card 3
Prompt
What index is understood in \(\sqrt a\)?
Answer
Index \(2\).
Card 4 of 20
EasyStudy card 4
Prompt
Rewrite \(\sqrt[n]{a}\) with a rational exponent.
Answer
\(a^{1/n}\).
Card 5 of 20
EasyStudy card 5
Prompt
For real numbers, what restriction applies to an even root?
Answer
Its radicand must be nonnegative.
Card 6 of 20
EasyStudy card 6
Prompt
Can an odd root have a negative radicand?
Answer
Yes; for example, \(\sqrt[3]{-8}=-2\).
Card 7 of 20
EasyStudy card 7
Prompt
How do you simplify \(\sqrt{72}\)?
Answer
\(\sqrt{36\cdot2}=6\sqrt2\).
Card 8 of 20
MediumStudy card 8
Prompt
When may two radical terms be added?
Answer
When they have the same index and same simplified radicand.
Card 9 of 20
MediumStudy card 9
Prompt
Simplify \(3\sqrt5+2\sqrt5\).
Answer
\(5\sqrt5\).
Card 10 of 20
MediumStudy card 10
Prompt
Can \(\sqrt2+\sqrt3\) be combined?
Answer
No; they are unlike radical terms.
Card 11 of 20
MediumStudy card 11
Prompt
State the product rule for square roots.
Answer
For nonnegative radicands, \(\sqrt a\sqrt b=\sqrt{ab}\).
Card 12 of 20
MediumStudy card 12
Prompt
State the quotient rule for square roots.
Answer
For valid real inputs with \(b>0\), \(\sqrt a/\sqrt b=\sqrt{a/b}\).
Card 13 of 20
MediumStudy card 13
Prompt
Does \(\sqrt{a+b}=\sqrt a+\sqrt b\) generally hold?
Answer
No. Radicals do not distribute over addition.
Card 14 of 20
MediumStudy card 14
Prompt
How do you rationalize \(1/\sqrt5\)?
Answer
Multiply by \(\sqrt5/\sqrt5\) to get \(\sqrt5/5\).
Card 15 of 20
MediumStudy card 15
Prompt
What is the conjugate of \(a+\sqrt b\)?
Answer
\(a-\sqrt b\).
Card 16 of 20
MediumStudy card 16
Prompt
Why do conjugates rationalize binomial denominators?
Answer
Their product is a difference of squares: \(a^2-b\).
Card 17 of 20
HardStudy card 17
Prompt
Simplify \(\sqrt{18x^2}\) for real \(x\).
Answer
\(3|x|\sqrt2\); the absolute value preserves the principal square root.
Card 18 of 20
HardStudy card 18
Prompt
When is \(\sqrt{x^2}=x\) valid without qualification?
Answer
When \(x\ge0\); in general, \(\sqrt{x^2}=|x|\).
Card 19 of 20
HardStudy card 19
Prompt
Rationalize \(1/(3+\sqrt2)\).
Answer
\((3-\sqrt2)/7\).
Card 20 of 20
HardStudy card 20
Prompt
What should be done before combining radical terms?
Answer
Simplify each radical completely, then compare indices and radicands.
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