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Lesson: Radical Equations

In this lesson, we will learn how to solve equations that include radical expressions, where the variable is the radicand, by raising each side to a power.

Sample Question Videos

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00:43
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Worksheet • 18 Questions • 6 Videos

Q1:

The natural way to solve √ π‘₯ + 9 βˆ’ 2 π‘₯ = 3 introduces an extraneous solution. What is that extraneous solution?

  • A π‘₯ = βˆ’ 1 1 4
  • B π‘₯ = 3
  • C π‘₯ = βˆ’ 2
  • D π‘₯ = 1 1 7
  • E π‘₯ = βˆ’ 3 4

Q2:

Solve √ π‘₯ βˆ’ 5 = βˆ’ 1 .

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

Q3:

Solve √ π‘₯ + 4 + 2 = 7 .

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

Q4:

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

Q5:

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

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

Q6:

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

Q7:

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

  • A900
  • B324
  • C30
  • D 27 000

Q8:

For what value of π‘˜ is π‘₯ = 1 introduced as an extraneous solution to the equation π‘₯ = √ π‘₯ + 3 + π‘˜ when it is solved in the natural way?

Q9:

In order to solve the equation , Fady started with

What solutions did Fady find?

Q10:

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

Q11:

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

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

Q12:

Solve √ 𝑦 = 4 0 .

Q13:

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

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

Q14:

Solve √ π‘₯ = 2 √ 7 + 5 .

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

Q15:

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

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

Q16:

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

Q17:

Solve √ 𝑦 = 8 . 5 .

Q18:

Consider the following argument for solving βˆ’ 3 = √ π‘₯ :

  1. βˆ’ 3 = √ π‘₯
  2. ( βˆ’ 3 ) = ο€Ί √ π‘₯   
  3. 9 = π‘₯ .

What mistake was made?

  • Asquaring βˆ’ 3 does not give 9
  • Bnot checking for extraneous solutions
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