Question

What two consecutive integers do -√17 , -√156 , and -√249 lie between? PLEASE Help

Answer 1

Start with
`√(17)`:

17 falls between the perfect squares of 16 and 25,

so
`√(17)` will fall between
`√(16)` and
`√(25)`, which is a funny way to say 4 and 5.

Now if that negative is really supposed to be there, then using the same logic,
`-√(17)` will fall between -4 and -5.

The key is to find the two perfect square closest to what's under the radical.

For
`√(156)`:

156 fall between 144 and 169, so
`√(156)` falls between
`√(144)` and
`√(169)`, or 12 and 13. Again, same note if you really meant
`-√(156)`.

For
`√(249)`:

Trying out some perfect squares:

`14^2 = 196`

`15^2=225`

`16^2=256`

We've found 225 and 256 are on either side of 249, so
`√(249)` falls between 15 and 16, again with the same note if you meant
`-√(249)`.