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Solve quadratics by taking square roots

9th grade (Year 10 in England) · 16 questions · Common Core: HSA.REI.B.4.B · England: GCSE Foundation Algebra

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  1. Question 1

    Solve (x + 7)² = 10, giving exact answers.

    • A. x = 7 ± √10
    • B. x = ±√59
    • C. x = −7 ± √10
    • D. x = −7 + √10

  2. Question 2

    Solve: x² − 5 = −4. Give both solutions, separated by a comma.

    x =

  3. Question 3

    Solve: (x + 1)² = 16. Give both solutions, separated by a comma.

    x =

  4. Question 4

    Solve (x + 1)² = 2, giving exact answers.

    • A. x = 1 ± √2
    • B. x = ±√3
    • C. x = −1 ± √2
    • D. x = −1 ± 2

  5. Question 5

    Solve: 5x² + 1 = 501. Give both solutions, separated by a comma.

    x =

  6. Question 6

    Solve: (x − 3)² = 81. Give both solutions, separated by a comma.

    x =

  7. Question 7

    Solve (x − 4)² = 5, giving exact answers.

    • A. x = 4 + √5
    • B. x = −4 ± √5
    • C. x = 4 ± 5
    • D. x = 4 ± √5

  8. Question 8

    Solve: 4x² = 16. Give both solutions, separated by a comma.

    x =

  9. Question 9

    Solve: (x + 2)² = 81. Give both solutions, separated by a comma.

    x =

  10. Question 10

    Solve (x + 1)² = 2, giving exact answers.

    • A. x = 1 ± √2
    • B. x = −1 ± √2
    • C. x = −1 ± 2
    • D. x = −1 + √2

  11. Question 11

    Solve: 4x² + 1 = 101. Give both solutions, separated by a comma.

    x =

  12. Question 12

    Solve: (x + 3)² = 64. Give both solutions, separated by a comma.

    x =

  13. Question 13

    Solve (x + 4)² = 3, giving exact answers.

    • A. x = −4 ± 3
    • B. x = −4 ± √3
    • C. x = −4 + √3
    • D. x = ±√19

  14. Question 14

    Solve: x² − 19 = 45. Give both solutions, separated by a comma.

    x =

  15. Question 15

    Solve: (x − 7)² = 81. Give both solutions, separated by a comma.

    x =

  16. Question 16

    Solve (x − 5)² = 11, giving exact answers.

    • A. x = 5 ± 11
    • B. x = 5 + √11
    • C. x = 5 ± √11
    • D. x = ±√36

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  1. x = −7 ± √10
  2. x = -1 or x = 1
  3. x = -5 or x = 3
  4. x = −1 ± √2
  5. x = -10 or x = 10
  6. x = -6 or x = 12
  7. x = 4 ± √5
  8. x = -2 or x = 2
  9. x = -11 or x = 7
  10. x = −1 ± √2
  11. x = -5 or x = 5
  12. x = -11 or x = 5
  13. x = −4 ± √3
  14. x = -8 or x = 8
  15. x = -2 or x = 16
  16. x = 5 ± √11