Lesson Worksheet: Solving Quadratic Equations: Taking Square Roots Mathematics • 8th Grade

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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 3𝑥−44=0 in ℝ, giving values to one decimal place.

  • A{8.1,−8.1}
  • B{−14.7,14.7}
  • C{23.0,−23.0}
  • D{3.8,−3.8}

Q2:

Find the solution set of the equation 4𝑥=𝑥9.

  • A{6}
  • B{36}
  • C{6,−6}
  • D{4,9}
  • E{36,−36}

Q3:

Find the solution set of the equation (𝑥−17)=0 in ℝ.

  • A{−17}
  • B{289}
  • C{17}
  • D{17,−17}

Q4:

If 𝑥−5,8=95,√𝑦, find all the possible values of 𝑥 and 𝑦.

  • A𝑥=10, 𝑦=8
  • B𝑥=10 or 𝑥=−10, 𝑦=512
  • C𝑥=100, 𝑦=512
  • D𝑥=10 or 𝑥=−10, 𝑦=8

Q5:

Solve 𝑥=2.

  • A𝑥=4
  • B𝑥=√2, 𝑥=−√2
  • C𝑥=2, 𝑥=−2
  • D𝑥=√2
  • E𝑥=2

Q6:

Solve the equation 𝑥+1=√3.

  • A𝑥=√3−1
  • B𝑥=√3+1, 𝑥=−√3+1
  • C𝑥=√3−1, 𝑥=−√3−1
  • D𝑥=√3, 𝑥=−√3
  • E𝑥=−√3−1

Q7:

Solve 𝑥=511.

  • A𝑥=115
  • B𝑥=511
  • C𝑥=√511, 𝑥=−√511
  • D𝑥=115, 𝑥=−115
  • E𝑥=511, 𝑥=−511

Q8:

Solve the equation 𝑥=16.

  • A𝑥=4, 𝑥=−4
  • B𝑥=8, 𝑥=−8
  • C𝑥=8
  • D𝑥=4
  • E𝑥=−4

Q9:

Solve the equation 𝑥+2=√3.

  • A𝑥=−2−√3𝑖
  • B𝑥=2−√3𝑖, 𝑥=−2−√3𝑖
  • C𝑥=2−√3𝑖
  • D𝑥=√3−2, 𝑥=−√3−2
  • E𝑥=√3−22, 𝑥=−√3−22

Q10:

Solve the equation (𝑥−2)=7.

  • A𝑥=9
  • B𝑥=3, 𝑥=−3
  • C𝑥=2+√7, 𝑥=2−√7
  • D𝑥=2+√7
  • E𝑥=2−√7

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