Worksheet: Solving Quadratic Equations: Taking Square Roots

In this worksheet, we will practice solving quadratic equations with no linear term using the square root property.

Q1:

Find the solution set of the equation (π‘₯βˆ’17)=0 in ℝ.

  • A { βˆ’ 1 7 }
  • B { 2 8 9 }
  • C { 1 7 }
  • D { 1 7 , βˆ’ 1 7 }

Q2:

Find the solution set of the equation 3π‘₯βˆ’44=0 in ℝ, giving values to one decimal place.

  • A { 8 . 1 , βˆ’ 8 . 1 }
  • B { βˆ’ 1 4 . 7 , 1 4 . 7 }
  • C { 2 3 . 0 , βˆ’ 2 3 . 0 }
  • D { 3 . 8 , βˆ’ 3 . 8 }

Q3:

Solve π‘₯=2.

  • A π‘₯ = 4
  • B π‘₯ = √ 2 , π‘₯ = βˆ’ √ 2
  • C π‘₯ = 2 , π‘₯ = βˆ’ 2
  • D π‘₯ = √ 2
  • E π‘₯ = 2

Q4:

Solve the equation π‘₯+1=√3.

  • A π‘₯ =  √ 3 βˆ’ 1
  • B π‘₯ =  √ 3 + 1 , π‘₯ = βˆ’  √ 3 + 1
  • C π‘₯ =  √ 3 βˆ’ 1 , π‘₯ = βˆ’  √ 3 βˆ’ 1
  • D π‘₯ =  √ 3 , π‘₯ = βˆ’  √ 3
  • E π‘₯ = βˆ’  √ 3 βˆ’ 1

Q5:

Solve π‘₯=511.

  • A π‘₯ = ο„ž 1 1 5
  • B π‘₯ = ο„ž 5 1 1
  • C π‘₯ = √ 5 1 1 , π‘₯ = βˆ’ √ 5 1 1
  • D π‘₯ = ο„ž 1 1 5 , π‘₯ = βˆ’ ο„ž 1 1 5
  • E π‘₯ = ο„ž 5 1 1 , π‘₯ = βˆ’ ο„ž 5 1 1

Q6:

Solve the equation π‘₯=16.

  • A π‘₯ = 4 , π‘₯ = βˆ’ 4
  • B π‘₯ = 8 , π‘₯ = βˆ’ 8
  • C π‘₯ = 8
  • D π‘₯ = 4
  • E π‘₯ = βˆ’ 4

Q7:

Solve (π‘₯+6)=4.

  • A π‘₯ = βˆ’ 4 or π‘₯=βˆ’8
  • B π‘₯ = 8 or π‘₯=βˆ’8
  • C π‘₯ = βˆ’ 5 or π‘₯=βˆ’7
  • D π‘₯ = 7 or π‘₯=5
  • E π‘₯ = 8 or π‘₯=4

Q8:

Solve the equation π‘₯+2=√3.

  • A π‘₯ = βˆ’ ο€Ώ  2 βˆ’ √ 3  𝑖
  • B π‘₯ = ο€Ώ  2 βˆ’ √ 3  𝑖 , π‘₯ = βˆ’ ο€Ώ  2 βˆ’ √ 3  𝑖
  • C π‘₯ = ο€Ώ  2 βˆ’ √ 3  𝑖
  • D π‘₯ =  √ 3 βˆ’ 2 , π‘₯ = βˆ’  √ 3 βˆ’ 2
  • E π‘₯ = √ 3 βˆ’ 2 2 , π‘₯ = βˆ’ √ 3 βˆ’ 2 2

Q9:

Solve the equation (π‘₯βˆ’2)=7.

  • A π‘₯ = 9
  • B π‘₯ = 3 , π‘₯ = βˆ’ 3
  • C π‘₯ = 2 + √ 7 , π‘₯ = 2 βˆ’ √ 7
  • D π‘₯ = 2 + √ 7
  • E π‘₯ = 2 βˆ’ √ 7

Q10:

Solve π‘₯+5=12.

  • A π‘₯ = √ 1 7
  • B π‘₯ = √ 1 2 βˆ’ 5
  • C π‘₯ = √ 7
  • D π‘₯ = √ 1 7 , π‘₯ = βˆ’ √ 1 7
  • E π‘₯ = √ 7 , π‘₯ = βˆ’ √ 7

Q11:

Determine the solution set of the equation 44π‘₯+9=0 given that π‘₯βˆˆβ„.

  • A βˆ…
  • B  3 √ 1 1 2 2 
  • C  βˆ’ 3 √ 1 1 2 2 
  • D  βˆ’ 3 √ 1 1 2 2 , 3 √ 1 1 2 2 

Q12:

Given that π‘₯=ο€»βˆš13βˆ’βˆš11ο‡ο€»βˆš13+√11ο‡οŠ¨, find the possible values of π‘₯.

  • A 2 √ 6
  • B √ 2
  • C √ 2 , βˆ’ √ 2
  • D 2 √ 6 , βˆ’ 2 √ 6

Q13:

Find all the possible values of π‘₯ for which 2π‘₯=50.

  • A √ 5 , βˆ’ √ 5
  • B10
  • C 5 , βˆ’ 5
  • D25

Q14:

Find all the values of π‘₯ which satisfy π‘₯3=48π‘₯.

  • A144
  • B12
  • C 1 2 , βˆ’ 1 2
  • D βˆ’ 1 2
  • E 1 4 4 , βˆ’ 1 4 4

Q15:

Solve π‘₯=4.

  • A π‘₯ = 8 or π‘₯=βˆ’8
  • B π‘₯ = 1 6 or π‘₯=βˆ’16
  • C π‘₯ = 2
  • D π‘₯ = 8
  • E π‘₯ = 2 or π‘₯=βˆ’2

Q16:

Solve π‘₯+5=14.

  • A π‘₯ = 2
  • B π‘₯ = 9 or π‘₯=βˆ’9
  • C π‘₯ = 3
  • D π‘₯ = 9
  • E π‘₯ = 3 or π‘₯=βˆ’3

Q17:

Find the solution set of the equation (π‘₯βˆ’5)=100 in β„š.

  • A βˆ…
  • B { 1 5 }
  • C { βˆ’ 1 5 , 5 }
  • D { βˆ’ 5 , 1 5 }

Q18:

Solve π‘₯=916.

  • A π‘₯ = 3 1 6 or π‘₯=βˆ’316
  • B π‘₯ = 3 1 6
  • C π‘₯ = 9 4 or π‘₯=βˆ’94
  • D π‘₯ = 3 4 or π‘₯=βˆ’34
  • E π‘₯ = 3 4

Q19:

Given that 9π‘₯+2=4, find the value of π‘₯, and state whether it is a rational or irrational number.

  • A Β± √ 6 3 , rational number
  • B Β± √ 2 3 , rational number
  • C Β± √ 2 3 , irrational number
  • D Β± √ 6 3 , irrational number
  • E Β± 2 9 , irrational number

Q20:

Write all of the values of π‘₯ which satisfy the equation 2π‘₯+8=13οŠͺ. If necessary, give your answer(s) to 4 significant figures.

  • A1.5
  • B1.257
  • C 1 2 . 5 7 , βˆ’ 1 2 . 5 7
  • D βˆ’ 1 . 2 5 7
  • E 1 . 2 5 7 , βˆ’ 1 . 2 5 7

Q21:

Find the solution set of the equation π‘₯=145 given that π‘₯βˆˆβ„.

  • A  √ 7 0 , βˆ’ √ 7 0 
  • B  √ 7 0 5 
  • C  √ 7 0 1 4 , βˆ’ √ 7 0 1 4 
  • D  √ 7 0 5 , βˆ’ √ 7 0 5 
  • E  √ 7 0 1 4 

Q22:

Solve π‘₯=0.36.

  • A π‘₯ = 0 . 3 6 or π‘₯=βˆ’0.36
  • B π‘₯ = 0 . 0 6 or π‘₯=βˆ’0.06
  • C π‘₯ = 6 or π‘₯=βˆ’6
  • D π‘₯ = 3 6 or π‘₯=βˆ’36
  • E π‘₯ = 0 . 6 or π‘₯=βˆ’0.6

Q23:

Find the solution set of (π‘₯+1)βˆ’64=0 in ℝ.

  • A { βˆ’ 2 1 , 3 }
  • B { βˆ’ 9 , 7 }
  • C { βˆ’ 1 , 1 }
  • D { βˆ’ 7 , 9 }
  • E { βˆ’ 3 , 2 1 }

Q24:

If ο€Ήπ‘₯βˆ’5,8=ο€Ί95,βˆšπ‘¦ο†οŠ¨οŽ’, find all the possible values of π‘₯ and 𝑦.

  • A π‘₯ = 1 0 , 𝑦 = 8
  • B π‘₯ = 1 0 or π‘₯=βˆ’10, 𝑦=512
  • C π‘₯ = 1 0 0 , 𝑦 = 5 1 2
  • D π‘₯ = 1 0 or π‘₯=βˆ’10, 𝑦=8

Q25:

Find the solution set of the equation 4π‘₯=π‘₯9.

  • A { 6 }
  • B { 3 6 }
  • C { 6 , βˆ’ 6 }
  • D { 4 , 9 }
  • E { 3 6 , βˆ’ 3 6 }

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