Approximate the square root of 11 by finding the two consecutive whole numbers that the square root lies between?

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Answer 1 · 2018-06-18T17:53:36

See a solution process below:

#1^2 = 1 xx 1 = 2#

#2^2 = 2 xx 2 = 4#

#3^2 = 3 xx 3 = 9#

#4^2 = 4 xx 4 = 16#

Therefore, #sqrt(11)# lies between #3# and #4#

Answer 2 · 2018-06-18T17:57:38

Good guess is:

#~~3 2/7 ~~ 3.29#

#sqrt9=3#
#sqrt16=4#

Our two consecutive whole numbers are 3,4

So the root must be in the range #3 < sqrt11 < 4#

Closer to 3 than 4 because #11-9=2# and #16-11=5#

Since there are 7 numbers between 9 and 16 and we are 2 numbers away from 9 let's guess #3 2/7 ~~ 3.29#

Pretty good guess, a calculator shows #sqrt11 ~~ 3.32#