The numbers a and b are consecutive positive integers, and a < square root 200 < b. What is the value of the product ab?
a < 14.14 < b
since a and b are consecutive integers
a = 14 and b = 15 ---- 14< 14.14 < 15 is true !
then ab = 14(15) = 210
To find the value of the product ab, we first need to determine the values of a and b.
We know that a and b are consecutive positive integers, which means they are just one apart. So we can represent them as a and (a + 1).
Now, let's consider the second condition: a < √200 < b.
To find the square root of 200, we can use a calculator or estimate it. The square root of 200 is approximately 14.142.
Since a < √200 < b, we can deduce that a = 14 and b = 15. (Since they are consecutive, and 14 < 14.142 < 15.)
Now, to find the value of the product ab, we simply multiply a and b:
ab = 14 * 15 = 210.
Therefore, the value of the product ab is 210.