Between what two consecutive integers do #sqrt50# lie?

1 Answer
Mar 13, 2018

Answer:

#sqrt50# is between #7# and #8#.

Explanation:

We can list out some of the squares and square roots that we know (I'll start from #5#):

#color(white){color(black)( (qquadqquad 5, qquadqquad sqrt25), (qquadqquad 6, qquadqquad sqrt36), (qquadqquad 7, qquadqquad sqrt49), (qquadqquad 8, qquadqquad sqrt64), (qquadqquad 9, qquadqquad sqrt81):}#

We can see that #sqrt50# would lie in between #sqrt49# and #sqrt64#, so that means that #sqrt50# is between #7# and #8#.

Using a calculator, we can validate this:

#sqrt50~~7.0710678...#