Algebra II - Simplifying Radicals

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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?

<p>2√5</p> Signup and view all the answers

What is √24 simplified?

<p>2√6</p> Signup and view all the answers

What is √27 simplified?

<p>3√3</p> Signup and view all the answers

What is √28 simplified?

<p>2√7</p> Signup and view all the answers

What is √48 simplified?

<p>4√3</p> Signup and view all the answers

What is √50 simplified?

<p>5√2</p> Signup and view all the answers

What is √63 simplified?

<p>3√7</p> Signup and view all the answers

What is √75 simplified?

<p>5√3</p> Signup and view all the answers

What is √125 simplified?

<p>5√5</p> Signup and view all the answers

What is √300 simplified?

<p>10√3</p> Signup and view all the answers

What is √243 simplified?

<p>9√3</p> Signup and view all the answers

What is √12 × √14 simplified?

<p>2√42</p> Signup and view all the answers

What is 4√75 simplified?

<p>20√3</p> Signup and view all the answers

What is √25x⁶ simplified?

<p>5x³</p> Signup and view all the answers

What is √18v³ simplified?

<p>3v√2v</p> Signup and view all the answers

What is √200x² simplified?

<p>10x√2</p> Signup and view all the answers

What is √64x⁹ simplified?

<p>8x⁴√x</p> Signup and view all the answers

What is √20a²b⁴ simplified?

<p>2ab²√5</p> Signup and view all the answers

What is √64x⁸y⁶ simplified?

<p>8x⁴y³</p> Signup and view all the answers

What is √250x⁹y¹⁰ simplified?

<p>5x⁴y⁵√10x</p> Signup and view all the answers

What is 2√18a⁶b² simplified?

<p>6a³b√2</p> Signup and view all the answers

What is -22√63x¹¹ simplified?

<p>-66x⁵√7x</p> Signup and view all the answers

What is ³√128x⁵ simplified?

<p>4x³√2x²</p> Signup and view all the answers

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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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