Determine whether the following regular tetrahedrons have an edge length that is a whole number, a rational number or irrational number.
The surface are of a tetrahedron is given by the equation: SA = √ 3s^2
Surface are of regular tetrahedron A = 1.5
Surface are of regular tetrahedron B = 4√3
Surface are of regular tetrahedron C = √3/100
Why square root is so confuse.please help me.
Thank you..
√3 s^2 = 3/2
s^2 = √3/2
clearly, s is not rational
√3s^2 = 4√3
s^2 = 4
s = 2, a whole number.
Now you try the other.
Square root can appear confusing because it involves finding the number that, when multiplied by itself, gives a certain value. This process of finding the square root is called "radical" and is denoted by the symbol (√).
In the case of determining whether the edge length of a regular tetrahedron is a whole number, rational number, or irrational number, we can use the formula for surface area to help us. The formula for the surface area of a regular tetrahedron is given as SA = √3s^2, where SA is the surface area and s is the edge length of the tetrahedron.
To determine whether the edge length is a whole number, rational number, or irrational number, we need to examine the values of the surface area for each tetrahedron.
Tetrahedron A: Surface area = 1.5
To find the edge length, we can rearrange the formula as s = √(SA/√3). Plugging in the given surface area, we have s = √(1.5/√3) ≈ 0.86603. Since this value is not a whole number, it is not a rational number either. Therefore, the edge length of tetrahedron A is an irrational number.
Tetrahedron B: Surface area = 4√3
Again, using the rearranged formula, we have s = √(SA/√3). Plugging in the given surface area, we have s = √((4√3)/√3) = √4 = 2. Since this value is a whole number, the edge length of tetrahedron B is a whole number.
Tetrahedron C: Surface area = √3/100
Using the rearranged formula, we have s = √(SA/√3). Plugging in the given surface area, we have s = √((√3/100)/√3) = √1/100 = 1/10. Since this value is a fraction, it is a rational number. Therefore, the edge length of tetrahedron C is a rational number.
So, in summary:
Tetrahedron A: Edge length is an irrational number.
Tetrahedron B: Edge length is a whole number.
Tetrahedron C: Edge length is a rational number.
I hope this explanation helps clarify the concept of square roots and how to determine the nature of numbers resulting from them. If you have any further questions, feel free to ask!