Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Evaluate Roots

Grade 8 · Algebra · Worksheet 3

  1. Emma is designing a community garden with a square plot that has an area of 256 square meters. She wants to build a cubic storage shed for gardening tools where the volume is exactly 512 cubic meters. What is the side length of the square garden, and what is the edge length of the cubic storage shed? Answer: ______________
  2. Noah is drawing a square on a coordinate grid. The square has vertices at (1, 1), (1, 6), (6, 1), and (6, 6). What is the side length of the square? Answer: ______________
  3. A cylindrical water tank has a diameter of 14 meters and a height of 10 meters. The tank is filled to 80% of its capacity. What is the volume of water in the tank in cubic meters? (Use π = 3.14)
    Answer: ______________
  4. √(729) + ∛(729) = ? Answer: ______________
  5. ∛(343) + √(196) = ? Answer: ______________
  6. Charlotte is designing a square mosaic tile. The area of the square tile is 289 square centimeters. What is the side length of the tile in centimeters? Answer: ______________
  7. Emma is designing a community garden with a square plot that has an area of 324 square meters. She wants to build a cubic storage shed for tools where the volume is exactly 1,000 cubic meters. What is the side length of the square garden, and what is the edge length of the cubic storage shed? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Evaluate Roots · Grade 8 · Worksheet 3

  1. Emma is designing a community garden with a square plot that has an area of 256 square meters. She wants to build a cubic storage shed for gardening tools where the volume is exactly 512 cubic meters. What is the side length of the square garden, and what is the edge length of the cubic storage shed? Answer: 16 and 8 Solution: Find the side length of the square garden. The area is 256 square meters, so we need to find the square root of 256. Since 16 × 16 = 256, the side length is 16 meters.
    Full step-by-step solution

    Step 1: Find the side length of the square garden. The area is 256 square meters, so we need to find the square root of 256. Since 16 × 16 = 256, the side length is 16 meters. Step 2: Find the edge length of the cubic storage shed. The volume is 512 cubic meters, so we need to find the cube root of 512. Since 8 × 8 × 8 = 512, the edge length is 8 meters. Step 3: The side length of the square garden is 16 meters, and the edge length of the cubic storage shed is 8 meters.

  2. Noah is drawing a square on a coordinate grid. The square has vertices at (1, 1), (1, 6), (6, 1), and (6, 6). What is the side length of the square? Answer: 5 Solution: Identify two adjacent vertices, for example (1, 1) and (1, 6). They share the same x-coordinate (1), so they are vertically aligned. Find the distance between them by subtracting the y-coordinates: 6 - 1 = 5.
    Full step-by-step solution

    Step 1: Identify two adjacent vertices, for example (1, 1) and (1, 6). They share the same x-coordinate (1), so they are vertically aligned. Step 2: Find the distance between them by subtracting the y-coordinates: 6 - 1 = 5. Step 3: Since the shape is a square, all sides are equal. The side length is 5 units. The answer is 5.

  3. A cylindrical water tank has a diameter of 14 meters and a height of 10 meters. The tank is filled to 80% of its capacity. What is the volume of water in the tank in cubic meters? (Use π = 3.14) Answer: 1230.88 Solution: Find the radius of the cylinder. The diameter is 14 meters, so the radius is 14 / 2 = 7 meters. Calculate the full volume of the cylinder using the formula V = πr²h.
    Full step-by-step solution

    Step 1: Find the radius of the cylinder. The diameter is 14 meters, so the radius is 14 / 2 = 7 meters. Step 2: Calculate the full volume of the cylinder using the formula V = πr²h. V = 3.14 × (7)² × 10 V = 3.14 × 49 × 10 V = 3.14 × 490 V = 1538.6 cubic meters Step 3: The tank is filled to 80% of its capacity. Calculate 80% of the full volume. Water volume = 80% × 1538.6 Water volume = 0.80 × 1538.6 Water volume = 1230.88 cubic meters The answer is 1230.88.

  4. √(729) + ∛(729) = ? Answer: 36 Solution: Find the square root of 729. Since 27 × 27 = 729, √(729) = 27. Find the cube root of 729.
    Full step-by-step solution

    Step 1: Find the square root of 729. Since 27 × 27 = 729, √(729) = 27. Step 2: Find the cube root of 729. Since 9 × 9 × 9 = 729, ∛(729) = 9. Step 3: Add the results: 27 + 9 = 36. The answer is 36.

  5. ∛(343) + √(196) = ? Answer: 21 Solution: Find the cube root of 343. Since 7 × 7 × 7 = 343, ∛(343) = 7 Find the square root of 196. Since 14 × 14 = 196, √(196) = 14 Add the results: 7 + 14 = 21 The answer is 21.
    Full step-by-step solution

    Step 1: Find the cube root of 343. Since 7 × 7 × 7 = 343, ∛(343) = 7 Step 2: Find the square root of 196. Since 14 × 14 = 196, √(196) = 14 Step 3: Add the results: 7 + 14 = 21 The answer is 21.

  6. Charlotte is designing a square mosaic tile. The area of the square tile is 289 square centimeters. What is the side length of the tile in centimeters? Answer: 17 Solution: Recall that the area of a square is side length squared, or A = s^2. We know the area is 289, so s^2 = 289. To find s, take the square root of both sides: s = sqrt(289).
    Full step-by-step solution

    Step 1: Recall that the area of a square is side length squared, or A = s^2. Step 2: We know the area is 289, so s^2 = 289. Step 3: To find s, take the square root of both sides: s = sqrt(289). Step 4: Find the perfect square root: 17 * 17 = 289, so sqrt(289) = 17. Step 5: The side length is 17 centimeters. The answer is 17.

  7. Emma is designing a community garden with a square plot that has an area of 324 square meters. She wants to build a cubic storage shed for tools where the volume is exactly 1,000 cubic meters. What is the side length of the square garden, and what is the edge length of the cubic storage shed? Answer: 18 and 10 Solution: Find the side length of the square garden. The area of a square is side × side = side². Given area = 324 m², so side² = 324.
    Full step-by-step solution

    Step 1: Find the side length of the square garden. The area of a square is side × side = side². Given area = 324 m², so side² = 324. Find the square root: side = sqrt(324) = 18 m. Step 2: Find the edge length of the cubic storage shed. The volume of a cube is edge × edge × edge = edge³. Given volume = 1,000 m³, so edge³ = 1,000. Find the cube root: edge = cube root of 1,000 = 10 m. Step 3: State both answers. The side length of the garden is 18 meters, and the edge length of the shed is 10 meters. The answer is 18 and 10.