Here we want to order from least to greatest the following expressions:
7.12 = 7.121212...
√75
√45
We will find that the order is: √45 < 7.12 < √75
remember that:
√x = y
such that:
y*y = x
From this, is easy to see that:
√45 < √75
Now to see where 7.1212... enters, we need to compute:
(7.1212...)*(7.1212...) = (7 + 0.1212...)*(7 + 0.1212...)
= 7*7 + 2*7*0.121212... + 0.1212...*0.1212...
= 49 + 2*7*0.121212... + 0.1212...*0.1212... > 45
So we know for sure that:
7.12 > √45
And 8*8 = 64 < 75
then:
7.12 < 8 = √64 < √75
For transitivity, we have:
7.12< √75
Then the order, from least to greatest, is:
√45 < 7.12 < √75
If you want to learn more, you can read:
https://brainly.com/question/21548193
