Root Equations Worksheets Grade 8

1. Liam is designing a square garden with an area of 289 square feet. He wants to build a stone path around it that increases the total area to 400 square feet. What will be the length of each side of the new, larger garden after the path is added?
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (12,0), and (12,5). A square is constructed such that one of its sides lies along the hypotenuse of the triangle, and the square is positioned entirely outside the triangle. What is the area of this square?
3. Maya is designing a square mosaic for her art project. The mosaic has an area of 196 square inches. She also needs to calculate the side length of a cube-shaped storage box that can hold exactly 729 cubic inches of art supplies. What is the side length of Maya's square mosaic, and what is the edge length of the cube storage box?

…and 3 more problems

1. Liam is designing a square garden with an area of 289 square feet. He wants to build a cube-shaped planter box where the volume is exactly 512 cubic feet. What is the side length of the square garden, and what is the edge length of the cube planter?
2. Mason is building a cube-shaped water tank for his school's science fair. The tank needs to hold exactly 512 cubic inches of water. He also wants to create a square observation window on one side of the tank with an area of 81 square inches. What is the edge length of the cube tank, and what is the side length of the square window?
3. ∛(125) × √(49) + 3² = ?

…and 3 more problems

1. ∛(x - 9) = 4
2. Liam is designing a square garden with an area of 256 square feet. He wants to build a path around it that increases the total area to 400 square feet. What will be the side length of the new garden including the path?
3. Hana is designing a square garden for her community project. The garden has an area of 324 square meters. She also wants to build a cube-shaped compost bin that can hold exactly 216 cubic meters of material. What is the side length of Hana's square garden, and what is the edge length of her cube-shaped compost bin?

…and 3 more problems