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Grade 11 Precal Radicals Cheat Sheet (DRAFT) by

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This is a draft cheat sheet. It is a work in progress and is not finished yet.

Radicals

A = coeffi­cient
n = index
√ = radical
x = radicand
  

Like vs. Unlike Radicals

√3 and 2√3
2√3 and 2√4
radicands are the same
radicands are not the same

Mixed vs. Entire

Mixed
Entire
2√3
√12
³√5
³√40
a≠1
a=1
 

Mixed to Entire

x√3) =√(x)(­x)(­x)(3)) =√3x²
³√4x) =³√(x)­(x)­(x)­((x­)(4­)(x)) = ³√4x
 

Entire to Mixed

√50 = (Factor tree) √(5)(5­)(2)) = 5√2
x√18⁴ = (Factor tree [18 = {2,9}] Perfect square) = x√9√2√x⁴√y = (3x)x²√2y) = 3x²√2y
Factor the radicand, so all factors are outside and look for perfect squares.
 
x√18x⁴y)
 

Entire to Mixed

√50 = (Factor tree) √(5)(5­)(2)) = 5√2
x√18x⁴y)