Solve ax^2 = c by taking square roots

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Ari solves x² = 196 on a puzzle card (the card insists it is easy). Two numbers work, one on each side of 0. What is the smaller solution?

   -14
2. 2.

   Bo solves x² = 121 with a freshly sharpened pencil. Two numbers work, one on each side of 0. What is the smaller solution?

   -11
3. 3.

   Esme's robot solves x² = 361 and beeps twice, once for each answer. Two numbers work, one on each side of 0. What is the smaller solution?

   -19
4. 4.

   In math club, Jun solves x² = 256. Two numbers work, one on each side of 0. What is the smaller solution?

   -16
5. 5.

   Kira lays 4 equal square tiles that cover 324 square inches in all. So 4x² = 324, where x is a side. Divide both sides by 4 first. What is the side length x?

   9
6. 6.

   Luz sews 9 equal square patches that cover 576 square inches in all. So 9x² = 576, where x is a side. Divide both sides by 9 first. What is the side length x?

   8
7. 7.

   Noah's greenhouse door has 25 equal square glass panes covering 900 square inches. So 25x² = 900, where x is a side. Divide both sides by 25 first. What is the side length x?

   6
8. 8.

   Pia's puzzle card says x² = -36. How many real solutions does it have?

   • Infinitely many solutions
   • Two real solutions
   • No real solution
   • One real solution
9. 9.

   Ren writes 4x² = -100 in orange crayon. How many real solutions does it have?

   • One real solution
   • Infinitely many solutions
   • Two real solutions
   • No real solution
10. 10.

    Zee's robot is stuck on -3x² = 0. How many real solutions does it have?

    • Two real solutions
    • No real solution
    • Infinitely many solutions
    • One real solution