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24

​
is not equal to a whole number. To approximate its value, we can first find which two perfect squares a square with an area of 24 square units is between. Start by finding the areas of the squares with the following whole number side lengths.
s =
24
​

Area = 24 units
2


Side Length (units) Area (units
2
)
3 3
2
=
4 4
2
=
5 5
2
=
6 6
2
=
7 7
2
=

1 answer

To find the side lengths of squares that have areas less than and greater than 24 square units, we can calculate the areas of squares with side lengths starting from whole numbers 1 through 7:

  1. Side Length = 1 unit:
    Area = \(1^2 = 1\) square unit

  2. Side Length = 2 units:
    Area = \(2^2 = 4\) square units

  3. Side Length = 3 units:
    Area = \(3^2 = 9\) square units

  4. Side Length = 4 units:
    Area = \(4^2 = 16\) square units

  5. Side Length = 5 units:
    Area = \(5^2 = 25\) square units

  6. Side Length = 6 units:
    Area = \(6^2 = 36\) square units

  7. Side Length = 7 units:
    Area = \(7^2 = 49\) square units

Now, we can identify the two perfect squares that the area of 24 square units is between:

  • The area of the square with a side length of 4 units is 16 square units (less than 24).
  • The area of the square with a side length of 5 units is 25 square units (greater than 24).

Thus, the area of 24 square units is between the perfect squares 16 (from a side length of 4) and 25 (from a side length of 5). Therefore, you can conclude that:

  • \(4 < \sqrt{24} < 5\)

To approximate \(\sqrt{24}\), you can calculate:

  • \(\sqrt{24} \approx 4.89\)

This suggests that the side length of a square that has an area of 24 square units is slightly less than 5 units.