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:

The natural way to solve 𝑥+92𝑥=3 introduces an extraneous solution. What is that extraneous solution?

  • A𝑥=117
  • B𝑥=3
  • C𝑥=114
  • D𝑥=2
  • E𝑥=34

Q2:

Solve 𝑥5=1.

  • A𝑥=6
  • B𝑥=4
  • C𝑥=36
  • D𝑥=16

Q3:

Solve 𝑥+4+2=7.

  • A𝑥=21
  • B𝑥=1
  • C𝑥=29
  • D𝑥=9
  • E𝑥=43

Q4:

Find the value of 𝑥 given that 𝑥=36.

Q5:

Find the solution set of the equation 𝑥+1=7, given that 𝑥.

  • A{512}
  • B{6}
  • C{216}
  • D{216}
  • E{512}

Q6:

Find the value of 𝑥 for which 1,225=400+𝑥.

  • A𝑥=4
  • B𝑥=100
  • C𝑥=9
  • D𝑥=225
  • E𝑥=169

Q7:

Given that 𝑥+34=4, find the value of 𝑥.

Q8:

For what value of 𝑘 is 𝑥=1 introduced as an extraneous solution to the equation 𝑥=𝑥+3+𝑘 when it is solved in the natural way?

Q9:

In order to solve the equation 𝑥+𝑥=6, Michael started with 𝑥+𝑥=6𝑥+𝑥6=0𝑥6=𝑥(𝑥6)=𝑥.

What solutions did Michael find?

Q10:

What is the solution set of the equation 𝑥+𝑥+20𝑥+100=5?

  • A23
  • B52
  • C52
  • D23

Q11:

Solve 𝑦=40.

  • A𝑦=40
  • B𝑦=80
  • C𝑦=20
  • D𝑦=40
  • E𝑦=1,600

Q12:

Find the value of 𝑥 given that 𝑥=10.

Q13:

Solve 𝑥=27+5.

  • A53207
  • B53+207
  • C33107
  • D53+107
  • E33+207

Q14:

Find the solution set of 𝑥9=4 in .

  • A{25,25}
  • B{625,625}
  • C{25}
  • D{625}

Q15:

Solve ||0.512||=𝑥.

Q16:

Solve 𝑦=8.5.

  • A𝑦=4.25
  • B𝑦=17
  • C𝑦=72.25
  • D𝑦=8.5
  • E𝑦=6.5

Q17:

Consider the following argument for solving 3=𝑥:

  1. 3=𝑥
  2. (3)=𝑥
  3. 9=𝑥.

What mistake was made?

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

Q18:

Find the solution set of the equation (14𝑥21)=400 given that 𝑥.

  • A4114
  • B114,4114
  • C27,3421
  • D4114,114
  • E4114,4114

Q19:

Solve 676+𝑥=7.

Q20:

Given that (5𝑥7)(25𝑥70𝑥+49)=1, find the value of 𝑥.

  • A65
  • B125
  • C47
  • D85

Q21:

Write all values of 𝑥 which satisfy the equation 𝑥+1𝑥=1.

  • A3
  • B0
  • C1
  • D0,1
  • E8

Q22:

Solve 𝑥7=3.

  • A𝑥=12
  • B𝑥=16
  • C𝑥=2
  • D𝑥=10
  • E𝑥=4

Q23:

Write all the values of 𝑥 which satisfy the equation 2𝑥1+𝑥=2.

Q24:

Daniel starts to solve 3+𝑥+6=2𝑥 as follows: 3+𝑥+6=2𝑥𝑥+6=2𝑥3𝑥+6=(2𝑥3)𝑥+6=4𝑥12𝑥+9.

Finish the solution for him.

  • A𝑥=14
  • B𝑥=13
  • C𝑥=3
  • D𝑥=2
  • E𝑥=12

Q25:

Squaring both sides of 𝑥+3=𝑥3 introduces an extraneous solution. What is that extraneous solution?

  • A𝑥=1
  • B𝑥=3
  • C𝑥=1
  • D𝑥=4
  • E𝑥=3

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