Square and cube roots Transitional Reasoning Practice

Questions

1. 1.

   An interior designer mounts a large square mirror with an area of $3.24\text{ m}^2$ on a gallery wall. Directly below the mirror, the designer installs three identical cubic display shelves placed side by side in a straight horizontal row. If each cubic shelf has a volume of $0.125\text{ m}^3$, what is the difference between the width of the mirror and the total combined width of the three shelves?

   • A) 1.3 m
   • B) 0.8 m
   • C) 0.3 m
   • D) 3.3 m
2. 2.

   An atmospheric research drone computes an altitude correction value, $C$, based on three sensor inputs: $P = \sqrt{\frac{81}{4}}$, $Q = \sqrt[3]{-\frac{64}{27}}$, and $R = \sqrt[3]{-125}$. The drone's flight software calculates this correction using the formula $C = 2P + 3Q - R$. What is the altitude correction value $C$?

   • A) 0
   • B) 8
   • C) 18
   • D) 10
3. 3.

   A logistics coordinator places three modular equipment cases side by side along a 40-decimeter workbench. The first case is a cube with a volume of $729\text{ dm}^3$, and the second case is a cube with a volume of $125\text{ dm}^3$. The third case has a square base with an area of $196\text{ dm}^2$. If each case rests on the bench so that one of its base edges runs along the length of the bench, how many decimeters of workbench length remain empty?

   • A) 28 dm
   • B) 16 dm
   • C) 10 dm
   • D) 12 dm
4. 4.

   A robotic rover navigates along a calibrated straight track marked with integer coordinates, starting at position 0. The rover first travels in the positive direction by a distance equal to the edge length of a cube with a volume of 343 cm$^3$. Next, it moves in the negative direction by a distance equal to the side length of a square with an area of 400 cm$^2$. Finally, after traveling in the positive direction by a distance equal to the edge length of a cube with a volume of 729 cm$^3$, at what coordinate on the track does the rover finish?

   • A) 14
   • B) -4
   • C) 36
   • D) 4
5. 5.

   An exhibition designer creates a flat square stage with an area of 256 m$^2$ and a cubic display case with a volume of 125 m$^3$. The designer plans to install neon lighting along the entire perimeter of the stage floor and along all twelve frame edges of the cubic display case. How many meters of neon lighting are needed in total?

   • A) 124 m
   • B) 104 m
   • C) 94 m
   • D) 84 m

Answers and step-by-step solutions appear after you finish the test.