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?

  • A 𝑥 = 1 1 7
  • B 𝑥 = 3
  • C 𝑥 = 1 1 4
  • D 𝑥 = 2
  • E 𝑥 = 3 4

Q2:

Solve 𝑥5=1.

  • A 𝑥 = 6
  • B 𝑥 = 4
  • C 𝑥 = 3 6
  • D 𝑥 = 1 6

Q3:

Solve 𝑥+4+2=7.

  • A 𝑥 = 2 1
  • B 𝑥 = 1
  • C 𝑥 = 2 9
  • D 𝑥 = 9
  • E 𝑥 = 4 3

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 { 5 1 2 }
  • B { 6 }
  • C { 2 1 6 }
  • D { 2 1 6 }
  • E { 5 1 2 }

Q6:

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

Q7:

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

  • A900
  • B30
  • C324
  • D27,000

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?

  • A 2 3
  • B 5 2
  • C 5 2
  • D 2 3

Q11:

Solve 𝑦=40.

Q12:

Find the value of 𝑥 given that 𝑥=10.

  • A30
  • B100
  • C10
  • D1,000
  • E 1 0 3

Q13:

Solve 𝑥=27+5.

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

Q14:

Find the solution set of 𝑥9=4 in .

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

Q15:

Solve ||0.512||=𝑥.

Q16:

Solve 𝑦=8.5.

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.

  • A 4 1 1 4
  • B 1 1 4 , 4 1 1 4
  • C 2 7 , 3 4 2 1
  • D 4 1 1 4 , 1 1 4
  • E 4 1 1 4 , 4 1 1 4

Q19:

Solve 676+𝑥=7.

Q20:

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

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

Q21:

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

  • A3
  • B0
  • C 1
  • D 0 , 1
  • E8

Q22:

Solve 𝑥7=3.

  • A 𝑥 = 1 2
  • B 𝑥 = 1 6
  • C 𝑥 = 2
  • D 𝑥 = 1 0
  • E 𝑥 = 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.

  • A 𝑥 = 1 4
  • B 𝑥 = 1 3
  • C 𝑥 = 3
  • D 𝑥 = 2
  • E 𝑥 = 1 2

Q25:

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

  • A 𝑥 = 1
  • B 𝑥 = 3
  • C 𝑥 = 1
  • D 𝑥 = 4
  • E 𝑥 = 3

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.