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Solving Problems Involving Radical Equations

Quiz by Dave Remerata

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20 questions
Show answers
  • Q1

    Luis walks 5 km due east and 8 km due north. How far is he from the starting point?

    √25 km

    √64 km

    √39 km


  • Q2

    Find the length of an edge of a cube given its surface area of 72 m2.

    2√3 m

    √2 m

    6√3 m

    6√12 m

  • Q3

    A taut rope starting from the top of a flagpole and tied to the ground is 15 m long. If the pole is 7 m high, how far is the rope from the base of the flagpole?

    11 √4 m

    16√4 m

    16 √11 m

    4 √11 m

  • Q4
  • Q5

    Five times the square root of 1 less than a number is equal to 3 more than the same number. Find the numbers.

    -17 and -2

    17 and 2

    15 and 4

    -15 and -4

  • Q6

    The square root of the sum of two consecutive odd integers is equal to 6. Find the larger integer.





  • Q7

    For an airplane flying above the earth, the approximate distance d (in miles) to the horizon is given by the equation d =√8000𝑎, where a is the altitude of the plane in miles. Determine the altitude of the plane if its distance to the horizon is 150 miles.

    4\frac{13}{16}\ mi

    1\frac{13}{16}\ mi

    3\frac{13}{16}\ mi

    2\frac{13}{16}\ mi

  • Q8

    The formula t = 1.11√𝐿 , gives the time t (in seconds) required for a pendulum of length L feet to swing through one back- and- forth- cycle. A grandfather’s pendulum completes one cycle in 1.28 seconds. To the nearest hundredths in feet, how long is the pendulum?

    1.33 ft

    1.23 ft

    1.22 ft

    1.63 ft

  • Q9

    Find the length of the side of a square if its diagonal is √2 cm.

    1 cm

    10 cm

    2 cm

    0.1 cm

  • Q10
  • Q11

    A man walks 4 meters to the east going to school and then walks 10 meters northward going to the church. How far is he from the starting point?

    4 √29 m

    3√29 m

    5 √29 m

    2√29 m

  • Q12

    If each side of a square garden is increased by 4 m, its area becomes 144 m2. What is the length of the side of the original square garden?

    19 m

    8 m

    16 m

    6 m

  • Q13

    A 26-foot ladder rests against a building and reaches a windowsill 24 feet above the ground. How far from the wall is the base of the ladder?

    13 ft

    12 ft

    11 ft

    10 ft

  • Q14
  • Q15

    Find the number such that twice its square root is 14.






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