Between what two consecutive integers do #sqrt650# lie?

1 Answer
Oct 17, 2015

Answer:

#sqrt650# lies between #25 # and #26#

Explanation:

Method 1: First we simplify the expression by prime factorising #650#

#sqrt650=sqrt(5*5*13*2)#

#=5sqrt(26)#

#sqrt26 = color(blue)(5.09#

So, #=5sqrt(26) = 5 xx color(blue)(5.09#

#approx25.495#

It can be observed that #sqrt650# lies between #25 # and #26#

Method 2
We can estimate the range of #sqrt650# if we have a good idea of squares of numbers.

  • #25^2=625#, from this result we get an idea that #sqrt650# is slightly higher that #25#, so we find #26^2#
  • #26^2= 676#

So #sqrt650# lies between #25# and #26#