Unit 8, Lesson 3
Square Roots
Accelerated 7
3.1
Warm-up
Find the area of each square and estimate the side lengths using your geometry toolkit. Then write the exact length for the sides of each square.
3.2
Activity
- Complete the tables with the missing side lengths and areas.
side length, 0.5 1.5 2.5 3.5 area, 1 4 9 16 side length, 4.5 5.5 6.5 7.5 area, 25 36 49 64 -
Plot the points, , on the coordinate plane shown here.
- Use the graph to estimate the side lengths of Squares A, B, and C from the previous activity. How do your estimates from the graph compare to the estimates you made earlier using your geometry toolkit?
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Use the graph to approximate .
3.3
Activity
- Find the area of each square and estimate their side lengths.
- Write the exact length for the side of each square.
- Which square has the larger area? Verify using your geometry toolkit.
Student Lesson Summary
We know that:
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because .
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because .
The value of must be between 3 units and 4 units because it is between the values of and .
There are 3 squares on a square grid, arranged in order of area, from smallest, on the left, to largest, on the right. The left most square is aligned to the grid and has side lengths of 3 with an area of 9. The middle square is tilted on the grid so that its sides are diagonal to the grid. The square is labeled with a side length of square root of 10 and an area of 10. The right most square is aligned to the grid and has side lengths of 4 with an area of 16.
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