Solve ax^2 = c by taking square roots

Answer Key - Grade 9 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Ari lays 3 equal square mats and a 5 square foot rug, covering 50 square feet: 3x² + 5 = 50, where x is a mat's side. What is x to the nearest tenth?

   3.9
2. 2.

   Esme solves 5x² + 12 = 47 on graph paper. What is the positive solution, to the nearest tenth?

   2.6
3. 3.

   A square garden has side length x feet. Jun solves 4x² - 7 = 33. What is the positive solution to the nearest tenth?

   3.2
4. 4.

   Luz's robot solves 4(x - 2)² - 9 = 27 without blinking. What is the larger solution?

   5
5. 5.

   In math club, Milo solves 3(x + 1)² + 4 = 196. What is the smaller solution?

   -9
6. 6.

   Noah solves 2(x - 6)² + 1 = 99, eraser ready. What is the smaller solution?

   -1
7. 7.

   Pia solves x² - 3 = 17 and wants the exact answer, root sign and all. Which gives both exact solutions?

   • x = √14 or x = -√14
   • x = 2√5 only
   • x = 2√5 or x = -2√5
   • x = 10 or x = -10
8. 8.

   Ren's math book asks for exact solutions of x² + 4 = 22. Which gives both exact solutions?

   • x = 3√2 or x = -3√2
   • x = √26 or x = -√26
   • x = 3√2 only
   • x = 9 or x = -9
9. 9.

   Tala's robot gives exact answers only. It is solving 3x² = 84. Which gives both exact solutions?

   • x = 2√7 only
   • x = 2√21 or x = -2√21
   • x = 14 or x = -14
   • x = 2√7 or x = -2√7
10. 10.

    Zee solves 4x² = 96 exactly, no calculator. Which gives both exact solutions?

    • x = 2√6 only
    • x = 2√6 or x = -2√6
    • x = 4√6 or x = -4√6
    • x = 12 or x = -12