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

Question

21352 views around the world

You can reuse this answer
Creative Commons License

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#