1. Find the exact length of each line segment.

   

2. Estimate the length of each line segment to the nearest tenth of a unit. Explain your reasoning.

1. Explain how you know that is a little more than 6.

2. Explain how you know that is a little less than 10.

3. Explain how you know that is between 5 and 6.

Select all the irrational numbers in the list.

Each grid square represents 1 square unit. What is the exact side length of the shaded square?

A square, not aligned to the horizontal or vertical gridlines, is on a square grid. The square is drawn such that the first vertex of the square is on the left side. The second vertex is 2 grid squares up and 3 grid squares right from the first vertex. The third vertex is 3 grid squares down and 2 grid squares right from the second vertex. The fourth vertex is 2 grid squares down and 3 grid squares left from the third vertex. The first vertex is 3 grid squares up and 2 grid squares left from the fourth vertex.

For each pair of numbers, which of the two numbers is larger? Estimate how many times larger.

1. and
2. and
3. and