Algebra II - Simplifying Radicals

Questions and Answers

What is the square root symbol (√) also known as?

Radicand

Root

Exponent

Radical (correct)

What is the term for the number under the √ radical?

Radicand

What is √8 simplified?

2√2

What is √20 simplified?

2√5 Signup and view all the answers

What is √24 simplified?

2√6 Signup and view all the answers

What is √27 simplified?

3√3 Signup and view all the answers

What is √28 simplified?

2√7 Signup and view all the answers

What is √48 simplified?

4√3 Signup and view all the answers

What is √50 simplified?

5√2 Signup and view all the answers

What is √63 simplified?

3√7 Signup and view all the answers

What is √75 simplified?

5√3 Signup and view all the answers

What is √125 simplified?

5√5 Signup and view all the answers

What is √300 simplified?

10√3 Signup and view all the answers

What is √243 simplified?

9√3 Signup and view all the answers

What is √12 × √14 simplified?

2√42 Signup and view all the answers

What is 4√75 simplified?

20√3 Signup and view all the answers

What is √25x⁶ simplified?

5x³ Signup and view all the answers

What is √18v³ simplified?

3v√2v Signup and view all the answers

What is √200x² simplified?

10x√2 Signup and view all the answers

What is √64x⁹ simplified?

8x⁴√x Signup and view all the answers

What is √20a²b⁴ simplified?

2ab²√5 Signup and view all the answers

What is √64x⁸y⁶ simplified?

8x⁴y³ Signup and view all the answers

What is √250x⁹y¹⁰ simplified?

5x⁴y⁵√10x Signup and view all the answers

What is 2√18a⁶b² simplified?

6a³b√2 Signup and view all the answers

What is -22√63x¹¹ simplified?

-66x⁵√7x Signup and view all the answers

What is ³√128x⁵ simplified?

4x³√2x² Signup and view all the answers

Study Notes

Radical Definition

Symbol for square root: √ (chiamate radicale)
The number under the radical symbol is known as the radicand

Simplifying Square Roots

√8 simplifies to 2√2
√20 simplifies to 2√5
√24 simplifies to 2√6
√27 simplifies to 3√3
√28 simplifies to 2√7
√48 simplifies to 4√3
√50 simplifies to 5√2
√63 simplifies to 3√7
√75 simplifies to 5√3
√125 simplifies to 5√5
√300 simplifies to 10√3
√243 simplifies to 9√3

Products and Variables in Radicals

√12×√14 simplifies to 2√42
√25x⁶ simplifies to 5x³
√18v³ simplifies to 3v√2v
√200x² simplifies to 10x√2
√64x⁹ simplifies to 8x⁴√x
√20a²b⁴ simplifies to 2ab²√5
√64x⁸y⁶ simplifies to 8x⁴y³
√250x⁹y¹⁰ simplifies to 5x⁴y⁵√10x
2√18a⁶b² simplifies to 6a³b√2
-22√63x¹¹ simplifies to -66x⁵√7x
³√128x⁵ simplifies to 4x³√2x²

Key Insights

Simplifying radicals involves breaking down numbers into their prime factors
Combining constants and variables outside the radical notation provides a clearer expression
Understanding these simplifications aids in solving algebraic equations involving radicals

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Description

Questo quiz se concentra sulla semplificazione dei radicali in Algebra II. Esplora simboli, radicandi e processi di semplificazione tramite flashcards. Impara a risolvere espressioni radicali con facilità.