Unit 4, Lesson 2
Square Roots and Cube Roots
Algebra 2
2.1
Warm-up
Find the area of square .
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Find the area of square .
Complete the table. Give the area of each square in square units, and give its exact side length in units.
| figure | A | B | C | D | E |
|---|---|---|---|---|---|
| area | 1 | ||||
| side length | 1 |
This table includes areas in square units and side lengths in units of some more squares. Complete the table.
| area | 9 | 23 | 89 | ||
|---|---|---|---|---|---|
| side length | 4 | 6.4 |
If a square has a side length of , then the area is . If a square has an area of , then the side length is . For a positive number , the square root of is defined as the positive number that squares to make , and it is written as . In other words, . We can also think of as a solution to the equation . This square has an area of because its sides have length :
Similarly, if a cube has an edge length of , then the volume is . If a cube has a volume of , then the edge length is . The number is defined as the number that cubes to make . In other words, . We can also think of as a solution to the equation . This cube has a volume of because its sides have a length of :