Answer:
3.15
Step-by-step explanation:
Let the unknown number be n.
Then 12n = √n + 36
We must eliminate the √ operator. One way to do this is to replace √n temporarily with x. Then 12n = 12x^2, and we have 12x^2 - x - 36 = 0. This is a quadratic with a= 12, b= -1 and c = -36
Solving for x using the quadratic formula:
1 plus or minus √(1 - 4(12)(-36)
x = ----------------------------------------------
2(12)
1 plus or minus √1729
x = -----------------------------------
24
1 plus or minus 41.58
x = -----------------------------------
24
Since x = √n, n must be a positive number. Thus,
1 + 41.58
x = ---------------- = 1.77
24
If x = 1.77 = √n, then n = 1.77^2 = 3.15.
Check: Is this true? A number multiplied by 12 is equal to the sum of the square root of that same number and 36.
12(3.15) = √3.15 + 36, or
37.8 = 1.77 + 36 = 37.77 This checks out.
The number is 3.15
