Checkpoint: the numbers that are not fractions

A square has sides of 1 unit. What is the area of the square drawn on its diagonal?

• 2 square units
• 1 square unit
• 4 square units

In the root 2 argument, why start with lowest terms?

• Then "both even" clashes with "no shared factor"
• A fraction not in lowest terms is not a fraction at all
• It makes the squaring easier to do by hand

Someone squares 1.4142 and gets 1.99996164. They say this shows root 2 is irrational. What is wrong?

• The squaring is wrong, 1.4142 squared is not that number
• Nothing is wrong, a square this near 2 settles it
• 1.4142 is a fraction, and one near miss proves nothing

At one stage of the spiral, the hypotenuse squares to 4. How long is it?

• Exactly 2 units
• Root 4, and it cannot be simpler
• Between 1 and 2

Root 3 lies in one gap. Which gap holds it?

• 1.6 to 1.7
• 1.7 to 1.8
• 1.5 to 1.6