Rational vs Irrational Worksheets Grade 8

1. √(2.25) + ∛(8) = ?
2. √(81) + ∛(64) - 4² = ?
3. Hana is building a square garden in her backyard. She wants the garden to have an area of exactly 50 square meters. Her friend Matiu says the side length of the garden will be a rational number because 50 is a whole number, but Hana thinks it might be irrational. Who is correct? Explain your reasoning by determining whether the side length is rational or irrational.

…and 5 more problems

1. √(2 + √(9)) = ?
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). The hypotenuse of this triangle is used as the diameter of a circle. What is the exact area of the circle? Express your answer in terms of π.
3. Emma is helping her science class calculate the dimensions of a rectangular terrarium for a project. The area of the terrarium must be exactly 125 square inches. The teacher says the length should be the square root of 75 inches, and the width should be the square root of 75 inches as well. Emma's friend Liam claims the side length of the terrarium will be a rational number because 75 ends in 5. Is Liam correct? Determine whether the side length is rational or irrational, and explain your reasoning.

…and 5 more problems

1. Charlotte is helping her science teacher prepare a demonstration. She needs to cut a wooden board into a square with an area of 98 square centimeters. Her teacher asks her to determine if the side length of the square is a rational or irrational number. What type of number is the side length? Explain your reasoning.
2. √(64) + ∛(125) - 2² = ?
3. Charlotte is helping her science class measure the side length of a square plot for a garden experiment. The area of the plot is 98 square feet. Charlotte needs to classify the side length as either rational or irrational. What type of number is the side length of the square plot, and why?

…and 5 more problems