Solve radical equations and equations with rational exponents, and check for fake answers

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Noah solves √(x² + 64) = 17 for x > 0 on a math club card. What is x?

   15
2. 2.

   Pia's robot solves √(x² + 81) = 15 for x > 0. What is x?

   12
3. 3.

   Ren solves √(x² + 576) = 25 for x > 0 in a math book. What is x?

   7
4. 4.

   A ball falls h feet in t = √h ÷ 4 seconds. Tala times a ball the science teacher drops from a third-floor window: 1.5 seconds. How many feet did it fall?

   36
5. 5.

   A ball falls h feet in t = √h ÷ 4 seconds. Zee drops a play ball from the top bleacher in science class; the fall takes 0.75 seconds. How many feet did it fall?

   9
6. 6.

   A ball falls h feet in t = √h ÷ 4 seconds. Ari times a ball the science teacher drops from the school roof: 1.25 seconds. How many feet did it fall?

   25
7. 7.

   Bo solves √(x + 2) + 4 = x on a math club card and checks each answer. Which choice gives every solution?

   • x = 7 only
   • x = 2 only
   • x = 7 and x = 2
   • no solution
8. 8.

   Esme's robot solves √(2x + 7) + 4 = x and checks each answer. Which choice gives every solution?

   • x = 9 only
   • x = 9 and x = 1
   • x = 1 only
   • no solution
9. 9.

   Jun solves √(5x + 6) − 2 = x on the class board and checks each answer. Which choice gives every solution?

   • x = 2 only
   • no solution, both answers fail
   • x = -1 only
   • x = 2 and x = -1
10. 10.

    Milo's robot solves 3(x − 1)^(3/4) = 24. What is x?

    17