Four square gardens have the following areas in square meters: 144, 32, 72, and 250. Which area has a rational number of meters as the side length?
To determine whether an area has a rational number side length, we need to find the square root of each area and see if it is a rational number.
The square root of 144 is 12, which is a rational number because it can be expressed as 12/1.
The square root of 32 is approximately 5.657, which is an irrational number because it cannot be expressed as a ratio of two integers.
The square root of 72 is approximately 8.485, which is an irrational number because it cannot be expressed as a ratio of two integers.
The square root of 250 is approximately 15.811, which is an irrational number because it cannot be expressed as a ratio of two integers.
Therefore, the only area that has a rational number as the side length is 144 square meters.
Booty
To determine which area has a rational number of meters as the side length, we need to check if the square root of each area is a rational number.
Let's calculate the square root of each area:
1. Square root of 144: √144 = 12 (which is rational).
2. Square root of 32: √32 ≈ 5.656854249492381 (which is irrational).
3. Square root of 72: √72 ≈ 8.48528137423857 (which is irrational).
4. Square root of 250: √250 ≈ 15.811388300841896 (which is irrational).
Based on these calculations, the only area with a rational number of meters as the side length is 144.
To determine which square garden has a rational number of meters as the side length, we need to find the area that has a perfect square (a number that can be expressed as the square of an integer) as its area.
To check if a number is a perfect square, we can calculate its square root and see if it is an integer.
Let's check each area to see if its square root is an integer:
1. For the first garden with an area of 144 square meters: √144 = 12. Since 12 is an integer, it is a perfect square.
2. For the second garden with an area of 32 square meters: √32 ≈ 5.657. Since 5.657 is not an integer, it is not a perfect square.
3. For the third garden with an area of 72 square meters: √72 ≈ 8.485. Since 8.485 is not an integer, it is not a perfect square.
4. For the fourth garden with an area of 250 square meters: √250 ≈ 15.811. Since 15.811 is not an integer, it is not a perfect square.
Therefore, the first garden with an area of 144 square meters has a rational number of meters as the side length.