MHB Number of Integers Between √19 and √90

  • Thread starter Thread starter prasadini
  • Start date Start date
  • Tags Tags
    Integers
AI Thread Summary
The discussion calculates the number of integers between √19 and √90, establishing that √19 is approximately 4.36 and √90 is about 9.49. By subtracting these two values, the difference is found to be 5.1279. Applying the floor function to this result yields the greatest integer less than or equal to 5.1279, which is 5. Therefore, there are 5 integers between √19 and √90.
prasadini
Messages
9
Reaction score
0
How many integers are there between √19 and √90
 
Mathematics news on Phys.org
$4\lt\sqrt{19}\lt5$ and $9\lt\sqrt{90}\lt10$
 
Subtract the lower number from the higher number.

√90 - √19 = 5.1279

Then use the "floor" function on 5.1279. If you are unfamiliar, floor(x) = the greatest integer <= x. (Basically round down)

So the number of integers between these two values is floor(5.1279)=5.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top