Question

how do i estimate 14 (square root) to the nearist integer

Answer 1

It is \[\sqrt{16}\]

Answer 2

Thanks :D

Answer 3

find the nearest number to your answer.
you want sqrt(14) - the closest whole number would be 16, since sqrt(16) is exactly 4.

f(x) = sqrt(x) = x^(1/2)
f(16) = sqrt(16) = 4

derive that:

f ' (x) = 1/2(x)^(-1/2) = 1/2(sqrt(x))
f ' (16) = 1/2*(sqrt(16)) = 1/2*4 = 1/8

1/8 is the slope of the graph.

so. sqrt(14) would be 4 - 2*(1/8) = 4.75
real sqrt(14) is 3.741657


the numbers in the answer represent :
4 is sqrt(16)
1/8 is the slope of the graph
2 is the difference between 16 and 14.

Answer 4

you would write down
3*3 = 9 and 3 = sqr(9)
4*4= 16 and 4= sqr(16)

then you would say 14 is closer to 16 (2 away) than 9 (5 away)
so pick 4

Answer 5

in other words \( \sqrt{14} \) will be between \( \sqrt{9}\) and \(\sqrt{16}\)
which means \( \sqrt{14} \) will be between 3 and 4
you just have to figure out if you should pick 3 or 4 (if you want the nearest integer)