Question

Compare the numbers √11 and 3.7. Use the symbols <,>,or=.

Answer 1

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Answer 2

Answer: Hi! here we want to compare the numbers
`√(11)` and
`3.7`

and we need to use <,> or =

So the first thing i would look is the square root.

we know that
`3^(2) = 9, 4^(2)  = 16`

so 3<
`√(11)` <4

now we can see
`3.7^(2)  = (3 + 0.7)*(3 + 0.7) = (3*3 + 2*0.7*3 + 0.7*0.7) =(9 + 6*0.7 + 0.7*0.7)`

is easy to see that
`0.7*6 \geq 0.5*6=3`

then
`3.7^(2)  = (9 + 0.7*6 + 0.7*0.7)  > (9 + 3 + 0.7*0.7) > 9 +3 = 12`

so 3.7^2 > 12, and 12>11

then:
`3.7 > √(11)`

You also can use a calculator, but i think this is not the idea of the problem.