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

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

Q2:

Solve 𝑥 5 = 1 .

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

Q3:

Solve 𝑥 + 4 + 2 = 7 .

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

Q4:

Find the value of 𝑥 given that 3 𝑥 = 3 6 .

Q5:

Find the solution set of the equation 𝑥 + 1 = 7 3 , given that 𝑥 .

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

Q6:

Find the value of 𝑥 for which 1 2 2 5 = 4 0 0 + 𝑥 .

Q7:

Given that 3 𝑥 + 3 4 = 4 , find the value of 𝑥 .

  • A 27 000
  • B324
  • C30
  • D900

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 , Fady started with

What solutions did Fady find?

Q10:

Given that 7 + 1 8 9 = 5 + 𝑥 , find 𝑥 .

Q11:

What is the solution set of the equation 𝑥 + 𝑥 + 2 0 𝑥 + 1 0 0 = 5 ?

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

Q12:

Solve 𝑦 = 4 0 .

Q13:

Find the value of 𝑥 given that 3 𝑥 = 1 0 .

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

Q14:

Solve 𝑥 = 2 7 + 5 .

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

Q15:

Find the solution set of 𝑥 9 = 4 1 2 in .

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

Q16:

Solve | | 0 . 5 1 2 | | = 𝑥 3 .

Q17:

Solve 𝑦 = 8 . 5 .

Q18:

Consider the following argument for solving 3 = 𝑥 :

  1. 3 = 𝑥
  2. ( 3 ) = 𝑥
  3. 9 = 𝑥 .

What mistake was made?

  • Anot checking for extraneous solutions
  • Bsquaring 3 does not give 9

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