How do you find the square root of 38.94?
2 Answers
Explanation:
You find it numerically. The actual square root is
The pattern with squares to get
#color(blue)((n+1)^2) = n^2 + 2n + 1#
#= color(blue)(n^2 + [(n) + (n+1)])#

Since
#60^2 = 3600# ,#61^2 = 60^2 + 60 + 61 = 3721# , and#62^2 = 61^2 + 61 + 62 = 3844# . 
Since
#3894  3844 < n# ,#3894# is not a perfect square. Furthermore, since#3894/100 = 38.94# , and#100 = 10^2# , if#3894# has no perfect square, neither does#38.94# . Therefore, it has an irregular decimal answer. 
From the above pattern,
#63^2 = 62^2 + 62 + 63 = 3969# , and#3894# is#40%# of the way from#3844# to#3969# . 
Since
#x^2# is approximately linear at high#x# , we can estimate the square root of#38.94# to be about#(62 + 0.4) xx 1/10 = color(blue)(6.24)# .
The actual square root is