Question

negative numbers do not have square roots in our number system. you can see why if you try to find a square root of -9. its impossible! a square root of -9 couldnt be positive because the square of a positive number is positive. it couldnt be negative either because the square of a negative number is also positive. certainly it isnt 0. √-9 just doesnt exist. it has no meaning. sometimes we say it is undefined. cross out the expressions which are undefined. √-100 √.81 √-.0025 -√100 √-.81 -√.0001 -√16 -√900 √-2.25 √-16 √-900 √2.25

Explanation:

Step1: Recall square - root property

The square root of a negative number $\sqrt{-a}$ ($a>0$) is undefined in the real - number system.

Step2: Analyze each expression

For $\sqrt{-100}$, since $- 100<0$, it is undefined. For $\sqrt{.81}=\sqrt{\frac{81}{100}} = 0.9$ (defined as $0.81>0$). For $\sqrt{-.0025}$, as $-.0025<0$, it is undefined. For $-\sqrt{100}=-10$ (defined as $100 > 0$). For $\sqrt{-.81}$, since $-.81<0$, it is undefined. For $-\sqrt{.0001}=-0.01$ (defined as $.0001>0$). For $-\sqrt{16}=-4$ (defined as $16>0$). For $-\sqrt{900}=-30$ (defined as $900>0$). For $\sqrt{-16}$, as $-16<0$, it is undefined. For $\sqrt{-900}$, since $-900<0$, it is undefined. For $\sqrt{-2.25}$, as $-2.25<0$, it is undefined. For $\sqrt{2.25} = 1.5$ (defined as $2.25>0$).

Answer:

$\sqrt{-100}$, $\sqrt{-.0025}$, $\sqrt{-.81}$, $\sqrt{-16}$, $\sqrt{-900}$, $\sqrt{-2.25}$