Lesson Worksheet: Radical Equations Mathematics • 10th Grade

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.


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

  • Aπ‘₯=117
  • Bπ‘₯=3
  • Cπ‘₯=βˆ’114
  • Dπ‘₯=βˆ’2
  • Eπ‘₯=βˆ’34


Solve √π‘₯βˆ’5=βˆ’1.

  • Aπ‘₯=6
  • Bπ‘₯=4
  • Cπ‘₯=36
  • Dπ‘₯=16


Solve √π‘₯+4+2=7.

  • Aπ‘₯=21
  • Bπ‘₯=1
  • Cπ‘₯=29
  • Dπ‘₯=9
  • Eπ‘₯=43


Find the value of π‘₯ given that √π‘₯=βˆ’βˆš36.


Find the solution set of the equation βˆ’βˆšπ‘₯+1=7, given that π‘₯βˆˆβ„.

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


Find the value of π‘₯ for which √1,225=√400+√π‘₯.

  • Aπ‘₯=4
  • Bπ‘₯=100
  • Cπ‘₯=9
  • Dπ‘₯=225
  • Eπ‘₯=169


Given that οŽ’ο„βˆšπ‘₯+34=4, find the value of π‘₯.


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?


In order to solve the equation π‘₯+√π‘₯=6, Daniel started with π‘₯+√π‘₯=6π‘₯+√π‘₯βˆ’6=0π‘₯βˆ’6=βˆ’βˆšπ‘₯(π‘₯βˆ’6)=π‘₯.

What solutions did Daniel find?


What is the solution set of the equation π‘₯+√π‘₯+20π‘₯+100=5?

  • Aο¬βˆ’23
  • Bο¬βˆ’52
  • C52
  • D23

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