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 rule

In the real - number system, $\sqrt{a}$ is undefined when $a<0$.

Step2: Analyze each expression

For $\sqrt{-100}$, since $-100<0$, it's undefined.
For $\sqrt{.81}$, $0.81 > 0$, $\sqrt{.81}=0.9$, it's defined.
For $\sqrt{-.0025}$, $-0.0025<0$, it's undefined.
For $-\sqrt{100}=-10$, it's defined.
For $\sqrt{-.81}$, $- 0.81<0$, it's undefined.
For $-\sqrt{.0001}=-0.01$, it's defined.
For $-\sqrt{16}=-4$, it's defined.
For $-\sqrt{900}=-30$, it's defined.
For $\sqrt{-16}$, since $-16<0$, it's undefined.
For $\sqrt{-900}$, since $-900<0$, it's undefined.
For $\sqrt{-2.25}$, since $-2.25<0$, it's undefined.
For $\sqrt{2.25} = 1.5$, it's defined.

Answer:

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