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Worksheet: Radical Equations

In this worksheet, we will practice solving equations that include radical expressions, where the variable is the radicand, by raising each side to a power.

Q1:

Find the value of π‘₯ given that 3 √ π‘₯ = βˆ’ √ 3 6 .

Q2:

Find the value of π‘₯ given that 3 √ π‘₯ = √ 1 6 .

Q3:

Find the value of π‘₯ given that 3 √ π‘₯ = βˆ’ √ 2 5 .

Q4:

Find the value of π‘₯ for which √ 1 2 2 5 = √ 4 0 0 + √ π‘₯ .

Q5:

Find the value of π‘₯ for which √ 4 4 1 = √ 8 1 + √ π‘₯ .

Q6:

Find the value of π‘₯ given that 3 √ π‘₯ = 1 0 .

  • A 100
  • B 10
  • C 1 0 3
  • D 1 000
  • E 30

Q7:

Find the value of π‘₯ given that 3 √ π‘₯ = 7 8 .

  • A 4 9 6 4
  • B 7 8
  • C 7 2 4
  • D 3 4 3 5 1 2
  • E 2 1 8

Q8:

Find the solution set of the equation βˆ’ √ π‘₯ + 1 = 7 3 , given that π‘₯ ∈ ℝ .

  • A { 5 1 2 }
  • B { βˆ’ 5 1 2 }
  • C { βˆ’ 6 }
  • D { βˆ’ 2 1 6 }
  • E { 2 1 6 }

Q9:

Find the solution set of the equation 3 √ π‘₯ + 4 = βˆ’ 3 3 , given that π‘₯ ∈ ℝ .

  • A  βˆ’ 2 7 8 
  • B  1 2 7 
  • C  βˆ’ 7 3 
  • D  βˆ’ 3 4 3 2 7 
  • E  3 4 3 2 7 

Q10:

Find the solution set of ο€Ί √ π‘₯ βˆ’ 9  = 4 1 2 in ℝ .

  • A { βˆ’ 6 2 5 , 6 2 5 }
  • B { 2 5 }
  • C { βˆ’ 2 5 , 2 5 }
  • D { 6 2 5 }

Q11:

Find the solution set of ο€Ί √ π‘₯ βˆ’ 2  = 5 1 2 in ℝ .

  • A { βˆ’ 7 2 9 , 7 2 9 }
  • B { 2 7 }
  • C { βˆ’ 2 7 , 2 7 }
  • D { 7 2 9 }

Q12:

Given that 3  √ π‘₯ + 3 4 = 4 , find the value of π‘₯ .

  • A 27 000
  • B324
  • C30
  • D900

Q13:

Solve √ 𝑦 = 8 . 5 .

Q14:

Solve | | √ βˆ’ 0 . 5 1 2 | | = √ π‘₯ 3 .

Q15:

Solve √ π‘₯ = 2 √ 7 + 5 .

  • A 5 3 + 1 0 √ 7
  • B 5 3 βˆ’ 2 0 √ 7
  • C 3 3 + 2 0 √ 7
  • D 5 3 + 2 0 √ 7
  • E 3 3 βˆ’ 1 0 √ 7

Q16:

Solve √ π‘₯ = √ 7 8 βˆ’ 3 .

  • A 8 7 βˆ’ 3 √ 7 8
  • B 8 7 + 6 √ 7 8
  • C 7 5 βˆ’ 6 √ 7 8
  • D 8 7 βˆ’ 6 √ 7 8
  • E 7 5 + 3 √ 7 8

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