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

Lesson: Solving Quadratics by Taking Square Roots

Video

05:02

Sample Question Videos

Worksheet • 25 Questions • 3 Videos

Q1:

Find the solution set of the equation 2 π‘₯ βˆ’ 2 0 = 0 2 in ℝ , giving values to one decimal place.

  • A { 3 . 2 , βˆ’ 3 . 2 }
  • B { 4 . 5 , βˆ’ 4 . 5 }
  • C { βˆ’ 1 0 . 0 , 1 0 . 0 }
  • D { 1 2 . 6 , βˆ’ 1 2 . 6 }

Q2:

Find the solution set of the equation 3 π‘₯ βˆ’ 4 4 = 0 2 in ℝ , giving values to one decimal place.

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

Q3:

Find the solution set of the equation 9 π‘₯ βˆ’ 1 6 = 0 2 in ℝ , giving values to one decimal place.

  • A { 1 . 3 , βˆ’ 1 . 3 }
  • B { 8 . 5 , βˆ’ 8 . 5 }
  • C { βˆ’ 1 . 8 , 1 . 8 }
  • D { 2 4 . 0 , βˆ’ 2 4 . 0 }

Q4:

Solve π‘₯ = 4 2 .

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

Q5:

Solve π‘₯ + 5 = 1 4  .

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

Q6:

If ο€Ή π‘₯ βˆ’ 5 , 8  = ο€Ί 9 5 , √ 𝑦  2 3 , find all the possible values of π‘₯ and 𝑦 .

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

Q7:

Solve π‘₯ = 2 2 .

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

Q8:

Solve the equation π‘₯ + 1 = √ 3 2 .

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

Q9:

Solve π‘₯ = 5 1 1 2 .

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

Q10:

Solve the equation π‘₯ = 1 6 2 .

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

Q11:

Solve ( π‘₯ + 6 ) = 4 2 .

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

Q12:

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

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

Q13:

Find the solution set of the equation 1 6 π‘₯ = π‘₯ 4 .

  • A { 8 , βˆ’ 8 }
  • B { 1 6 , 4 }
  • C { 8 }
  • D { 6 4 }
  • E { 6 4 , βˆ’ 6 4 }

Q14:

Find the solution set of the equation 1 π‘₯ = π‘₯ 4 .

  • A { 2 , βˆ’ 2 }
  • B { 1 , 4 }
  • C { 2 }
  • D { 4 }
  • E { 4 , βˆ’ 4 }

Q15:

Find the solution set of the equation ( π‘₯ βˆ’ 5 ) = 1 0 0 2 in β„š .

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

Q16:

Determine the solution set of the equation 4 4 π‘₯ + 9 = 0 2 given that π‘₯ ∈ ℝ .

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

Q17:

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

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

Q18:

Find all the possible values of π‘₯ for which 2 π‘₯ = 5 0 2 .

  • A 5 , βˆ’ 5
  • B 25
  • C 10
  • D √ 5 , βˆ’ √ 5

Q19:

Given that π‘₯ = ο€» √ 1 3 βˆ’ √ 1 1  ο€» √ 1 3 + √ 1 1  2 , find the possible values of π‘₯ .

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

Q20:

Solve the equation π‘₯ + 2 = √ 3 2 .

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

Q21:

Solve the equation ( π‘₯ βˆ’ 2 ) = 7 2 .

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

Q22:

Find all the values of π‘₯ which satisfy π‘₯ 3 = 4 8 π‘₯ .

  • A 1 2 , βˆ’ 1 2
  • B144
  • C12
  • D 1 4 4 , βˆ’ 1 4 4
  • E βˆ’ 1 2

Q23:

Solve π‘₯ + 5 = 1 2 2 .

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

Q24:

Solve π‘₯ = 9 1 6 2 .

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

Q25:

Find the solution set of 2 π‘₯ = 3 2 π‘₯ 3 in ℝ .

  • A { 0 , 4 , βˆ’ 4 }
  • B { 0 , 1 6 , βˆ’ 1 6 }
  • C { 4 , βˆ’ 4 }
  • D { 4 }
  • E { 1 6 , βˆ’ 1 6 }
Preview