Answer: Hi! here we want to compare the numbers [tex]\sqrt{11}[/tex] and [tex]3.7[/tex]
and we need to use <,> or =
So the first thing i would look is the square root.
we know that [tex]3^{2} = 9, 4^{2} = 16[/tex]
so 3< [tex]\sqrt{11}[/tex] <4
now we can see [tex]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)[/tex]
is easy to see that [tex]0.7*6 \geq 0.5*6=3[/tex]
then [tex]3.7^{2} = (9 + 0.7*6 + 0.7*0.7) > (9 + 3 + 0.7*0.7) > 9 +3 = 12[/tex]
so 3.7^2 > 12, and 12>11
then: [tex]3.7 > \sqrt{11}[/tex]
You also can use a calculator, but i think this is not the idea of the problem.
