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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 − 6)² = 1. Give both solutions, separated by a comma.

    x =

  2. Question 2

    Solve (x + 6)² = 10, giving exact answers.

    • A. x = −6 + √10
    • B. x = −6 ± √10
    • C. x = −6 ± 10
    • D. x = 6 ± √10

  3. Question 3

    Solve: x² − 12 = −11. Give both solutions, separated by a comma.

    x =

  4. Question 4

    Solve: (x + 8)² = 16. Give both solutions, separated by a comma.

    x =

  5. Question 5

    Solve (x + 6)² = 3, giving exact answers.

    • A. x = −6 + √3
    • B. x = 6 ± √3
    • C. x = −6 ± √3
    • D. x = ±√39

  6. Question 6

    Solve: 5x² + 1 = 321. Give both solutions, separated by a comma.

    x =

  7. Question 7

    Solve: (x + 2)² = 9. Give both solutions, separated by a comma.

    x =

  8. Question 8

    Solve (x + 6)² = 7, giving exact answers.

    • A. x = −6 ± 7
    • B. x = −6 ± √7
    • C. x = ±√43
    • D. x = 6 ± √7

  9. Question 9

    Solve: 2x² − 16 = 184. Give both solutions, separated by a comma.

    x =

  10. Question 10

    Solve: (x − 2)² = 25. Give both solutions, separated by a comma.

    x =

  11. Question 11

    Solve (x + 6)² = 11, giving exact answers.

    • A. x = 6 ± √11
    • B. x = −6 ± √11
    • C. x = ±√47
    • D. x = −6 + √11

  12. Question 12

    Solve: 4x² − 13 = 23. Give both solutions, separated by a comma.

    x =

  13. Question 13

    Solve: (x + 5)² = 16. Give both solutions, separated by a comma.

    x =

  14. Question 14

    Solve (x + 6)² = 10, giving exact answers.

    • A. x = ±√46
    • B. x = −6 + √10
    • C. x = −6 ± √10
    • D. x = −6 ± 10

  15. Question 15

    Solve: x² − 16 = 9. Give both solutions, separated by a comma.

    x =

  16. Question 16

    Solve: (x − 7)² = 36. Give both solutions, separated by a comma.

    x =

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Answer key: Solve quadratics by taking square roots

  1. 1. x = 5 or x = 7

  2. 2. B. x = −6 ± √10

  3. 3. x = -1 or x = 1

  4. 4. x = -12 or x = -4

  5. 5. C. x = −6 ± √3

  6. 6. x = -8 or x = 8

  7. 7. x = -5 or x = 1

  8. 8. B. x = −6 ± √7

  9. 9. x = -10 or x = 10

  10. 10. x = -3 or x = 7

  11. 11. B. x = −6 ± √11

  12. 12. x = -3 or x = 3

  13. 13. x = -9 or x = -1

  14. 14. C. x = −6 ± √10

  15. 15. x = -5 or x = 5

  16. 16. x = 1 or x = 13