# How do you order the following from least to greatest sqrt2, 2.1, -sqrt4, 0, -5/2?

May 3, 2017

$- \frac{5}{2} , - \sqrt{4} , 0 , \sqrt{2} , 2.1$

#### Explanation:

$\sqrt{2} , 2.1 , - \sqrt{4} , 0 , - \frac{5}{2}$

ordering these can be done without using a calculator.

first, convert all numbers to square roots:

$\sqrt{2} = \sqrt{2}$

$2.1 = \sqrt{{2.1}^{2}} = \sqrt{2.1 \cdot 2.1} = \sqrt{4.41}$

$- \sqrt{4} = - \sqrt{4}$

$0 = \sqrt{0}$

$- \frac{5}{2} = - \sqrt{{5}^{2} / {2}^{2}} = - \sqrt{\frac{25}{4}} = - \sqrt{6.25}$

$\sqrt{2} , \sqrt{4.41} , - \sqrt{4} , \sqrt{0} , - \sqrt{6.25}$

then order them:

$- \sqrt{4} , \sqrt{0} , \sqrt{2} , \sqrt{4.41} , - \sqrt{6.25}$

you can then convert these back to the original numbers:

$- \frac{5}{2} , - \sqrt{4} , 0 , \sqrt{2} , 2.1$