# How do you order the following from least to greatest 1.9, 2sqrt(11/4), sqrt5, 3 5/6?

Jan 30, 2017

$1.9 , \sqrt{5} , 2 \sqrt{\frac{11}{4}} , 3 \frac{5}{6} ,$

#### Explanation:

$\therefore 2 \times \sqrt{\frac{11}{4}} = 3.3166$

$\therefore \sqrt{5} = 2.2361$

$\therefore 3 \frac{5}{6} = 3.833333$

Jan 30, 2017

$1.9 \text{ "sqrt5" "2sqrt(11/4)" } 3 \frac{5}{6}$

#### Explanation:

Quite a neat way of deciding on the order without using a calculator to find the exact values, is to square each term to get rid of the square roots.

We can also just work with approximations, as the numbers are quite different in size

$1.9 \text{ " 2sqrt(11/4)" "sqrt5" } 3 \frac{5}{6}$

$1.9 \approx 2 \rightarrow {2}^{2} = 4 \text{ }$ (this is a bit bigger than its exact answer)

${\left(2 \sqrt{\frac{11}{4}}\right)}^{2} = 4 \times \frac{11}{4} = 11$

${\left(\sqrt{5}\right)}^{2} = 5$

$3 \frac{5}{6} \approx 4 \rightarrow {4}^{2} = 16$

The squares in ascending order are $\text{ "4" "5" "11" } 16$

So the correct order of the original numbers is

$1.9 \text{ "sqrt5" "2sqrt(11/4)" } 3 \frac{5}{6}$

(Thanks to Tony B for sharing this method a while back)