IM 8.8.4 Lesson: Square Roots on the Number Line

What do you notice? What do you wonder?

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[/img]

Estimate the length of the line segment to the nearest tenth of a unit (each grid square is 1 square unit).

[img]data:image/png;base64,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[/img]

Find the exact length of the segment.

[size=150]Diego said that he thinks that[math]\sqrt{3}\approx2.5[/math].[/size][br][br][img]data:image/png;base64,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[/img][br]Use the square to explain why 2.5 is not a very good approximation for [math]\sqrt{3}[/math].

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 [math]\sqrt{3}[/math].

Use the fact that [math]\sqrt{3}[/math] is a solution to the equation [math]x^2=3[/math] to find a decimal approximation of [math]\sqrt{3}[/math] whose square is between 2.9 and 3.1.

[size=150]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.[/size][br][img]data:image/png;base64,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[/img][br]What should the side length of the smaller square be so that half of the area is grass and half is water?

Information: IM 8.8.4 Lesson: Square Roots on the Number Line