Rational vs Irrational Worksheets Grade 8

Decimals

Number Types

Each printable worksheet below is a full page of practice problems and comes with an answer key that explains how to solve every problem, step by step. Open a worksheet and use the Print / Save as PDF button to download it.

Worksheet 1

8 problems
  1. Aroha is building a square patio in her backyard. The area of the patio is 45 square meters. She needs to know if the side length of the patio is a rational or irrational number so she can order the correct number of paving stones. What type of number is the side length of Aroha's patio?
  2. A rectangular garden is drawn on a coordinate plane with corners at (0,0), (12,0), (12,5), and (0,5). A diagonal path is drawn from (0,0) to (12,5), and a circular fountain is placed at the exact midpoint of this diagonal. What is the distance from the fountain to the corner at (12,0)? Round your answer to the nearest tenth.
  3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A circle is drawn such that its diameter is equal to the length of the hypotenuse of this triangle. What is the area of the circle? (Use π = 3.14)

…and 5 more problems

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Worksheet 2

7 problems
  1. Charlotte draws a square on a coordinate plane with vertices at (0,0), (9,0), (9,9), and (0,9). She then draws a diagonal from (0,0) to (9,9). At the midpoint of this diagonal, she places a small circle. A second circle is drawn with its center at (9,0) and a radius equal to the distance from (9,0) to the midpoint of the diagonal. Determine whether the radius of the second circle is rational or irrational, and explain why.
  2. Is √(196) + ∛(216) rational or irrational?
  3. Is √(121) + ∛(216) rational or irrational? Explain.

…and 4 more problems

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Worksheet 3

8 problems
  1. Is √(121) + ∛(216) rational or irrational?
  2. Mere is designing a square garden in her backyard. She draws the garden on a coordinate plane with corners at (0,0), (8,0), (8,8), and (0,8). She then draws a diagonal path from (0,0) to (8,8) and places a circular birdbath at the exact midpoint of this diagonal. The radius of the birdbath is exactly half the distance from the midpoint to the corner at (8,0). Will the area of the circular birdbath be a rational or irrational number? Explain your reasoning.
  3. Is sqrt(121) + sqrt(49) rational or irrational? Explain why.

…and 5 more problems

Open & Print Worksheet 3

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