Irrational Numbers Worksheet with Answer Key

What's on the worksheet

1. Decide if each number is rational or irrational, writing the rational ones another way:
   \sqrt{361}\sqrt{363}\sqrt{0.0081}\sqrt{16.9}\sqrt{\frac{98}{32}}
2. Work out each number as far as you can, then decide with a reason:
   \sqrt{2} \times \sqrt{8} + \sqrt{3}(\sqrt{5} + 1)^2 - 2\sqrt{5}\sqrt{12} \times \sqrt{3} - 6\dfrac{2}{3}\sqrt{10} \times \sqrt{10}\sqrt{6} \times \sqrt{15}
3. Find which whole numbers from 40 to 70 have a rational square root, and count the irrational ones.
4. Show Mei is wrong about the square root of 0.9 by squaring her answer.
5. Word problem: the exact circumference of a clock face, versus Lucas's 22 cm.
6. Follow a proof by contradiction that the square root of 2 is irrational, using last digits.