Irrational Numbers Test – Grade 8 Math (Printable PDF)

Question 1 Sort the numbers (3 points)

Classify each number as rational or irrational. (½ point each)

1. −5.25
2. √72
3. √169
4. 0.909090…
5. 2π
6. √916

Question 2 Decimals and fractions (3 points)

Write each as a fraction in lowest terms.

1. 0.6125 (1 point)
2. 0.135135135… (2 points)

Question 3 Estimating a root (2 points)

Locate √61 between whole numbers, then round it to one decimal place.

Question 4 Points on a number line (3 points)

Four points, A through D, sit on this number line. Three of them are the locations of √11, √13 and √15. Identify each and justify with squares.

Question 5 Order the numbers (2 points)

Order from least to greatest and justify: √23, 4.8, 479, 4.79.

Question 6 The mural (3 points)

A square mural has an area of 90 square feet.

1. The side lies between which pair of neighboring whole numbers? (1 point)
2. Estimate the side in feet, rounded to one decimal place. (1 point)
3. Is the side exactly 9.5 feet? Explain. (1 point)

Question 7 Always irrational? (2 points)

Arlo claims that the product of two irrational numbers is always irrational. Give one example that shows his claim is false, and show the calculation.

Question 8 A late-starting repeat (2 points)

Write 0.2777… as a fraction in lowest terms.