Lesson Worksheet: Radical Equations Mathematics • 10th Grade

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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+9−2𝑥=3 introduces an extraneous solution. What is that extraneous solution?

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

Q2:

Solve √𝑥−5=−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∈ℝ.

  • 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, Daniel started with 𝑥+√𝑥=6𝑥+√𝑥−6=0𝑥−6=−√𝑥(𝑥−6)=𝑥.

What solutions did Daniel find?

Q10:

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

  • A−23
  • B−52
  • C52
  • D23

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