IM 8.8.4 Lesson: Square Roots on the Number Line
What do you notice? What do you wonder?
Estimate the length of the line segment to the nearest tenth of a unit (each grid square is 1 square unit).
Find the exact length of the segment.
Diego said that he thinks that.
Use the square to explain why 2.5 is not a very good approximation for .
Find a point on the number line that is closer to √3.
Draw a new square on the axes and use it to explain how you know the point you plotted is a good approximation for .
Use the fact that is a solution to the equation to find a decimal approximation of whose square is between 2.9 and 3.1.
A farmer has a grassy patch of land enclosed by a fence in the shape of a square with a side length of 4 meters. To make it a suitable home for some animals, the farmer would like to carve out a smaller square to be filled with water, as in the figure.
What should the side length of the smaller square be so that half of the area is grass and half is water?