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Worksheet: Radical Equations

Q1:

What is the solution set of the equation π‘₯ + √ π‘₯ + 2 0 π‘₯ + 1 0 0 = 5 2 ?

  • A  2 3 
  • B  5 2 
  • C  βˆ’ 2 3 
  • D  βˆ’ 5 2 

Q2:

What is the solution set of the equation βˆ’ 9 π‘₯ + √ 2 5 π‘₯ βˆ’ 5 0 π‘₯ + 2 5 = 1 0 2 ?

  • A  1 5 4 
  • B  5 1 4 
  • C  βˆ’ 1 5 4 
  • D  βˆ’ 5 1 4 

Q3:

Solve √ π‘₯ + 4 + 2 = 7 .

  • A π‘₯ = 2 9
  • B π‘₯ = 4 3
  • C π‘₯ = 1
  • D π‘₯ = 2 1
  • E π‘₯ = 9

Q4:

Solve √ π‘₯ βˆ’ 5 = βˆ’ 1 .

  • A π‘₯ = 6
  • B π‘₯ = 3 6
  • C π‘₯ = 4
  • D π‘₯ = 1 6

Q5:

Find the solution set of the equation 3 3  ( 1 4 π‘₯ βˆ’ 2 1 ) = √ 4 0 0 2 given that π‘₯ ∈ ℝ .

  • A  βˆ’ 1 1 4 , βˆ’ 4 1 1 4 
  • B  4 1 1 4 
  • C  4 1 1 4 , βˆ’ 4 1 1 4 
  • D  4 1 1 4 , 1 1 4 
  • E  βˆ’ 2 7 , 3 4 2 1 

Q6:

Find the solution set of the equation 3 3  ( 2 2 π‘₯ + 2 1 ) = √ 3 6 1 2 given that π‘₯ ∈ ℝ .

  • A  2 0 1 1 , 1 1 1 
  • B  βˆ’ 1 1 1 
  • C  βˆ’ 1 1 1 , 1 1 1 
  • D  βˆ’ 1 1 1 , βˆ’ 2 0 1 1 
  • E  βˆ’ 1 7 , βˆ’ 4 1 2 1 

Q7:

Solve 3 √ 6 7 6 + π‘₯ = 7 .

Q8:

Given that √ 7 + 1 8 9 = 5 + π‘₯ , find π‘₯ .

Q9:

Given that √ 8 + 1 1 3 = 9 + π‘₯ , find π‘₯ .

Q10:

Write all values of π‘₯ which satisfy the equation √ π‘₯ + 1 βˆ’ π‘₯ = 1 .

  • A βˆ’ 1
  • B0
  • C3
  • D 0 , βˆ’ 1
  • E8

Q11:

Solve √ 𝑦 = 4 0 .

Q12:

Solve √ π‘₯ βˆ’ 7 = 3 .

  • A π‘₯ = 2
  • B π‘₯ = 1 0
  • C π‘₯ = 4
  • D π‘₯ = 1 6
  • E π‘₯ = 1 2

Q13:

Write all the values of π‘₯ which satisfy the equation √ 2 π‘₯ βˆ’ 1 + π‘₯ = 2 .