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For any nonnegative real number c, (sqrtc)^(2)= _____
A. sqrtc
B. c
C. 1
D. c^(2)

For any nonnegative real number $c$ , $(\sqrt{c})^{2}=$ _____ $\newline$ $\text{A. } \sqrt{c}$ $\newline$ $\text{B. } c$ $\newline$ $\text{C. } 1$ $\newline$ $\text{D. } c^{2}$

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Does (x, y) satisfy the inequality?

Full solution

Q. For any nonnegative real number

c

,

(\sqrt{c})^{2}=

_____

\newline

\text{A. } \sqrt{c}

\newline

\text{B. } c

\newline

\text{C. } 1

\newline

\text{D. } c^{2}

Substitute $c$ with $4$ : Substitute $c$ with a nonnegative number to check the property, let's use $c = 4$ . So, $(\sqrt{4})^2$ should simplify. $\newline$ Calculation: $(\sqrt{4})^2 = (2)^2 = 4$ .
Generalize the property: Now, let's generalize the property. For any nonnegative real number $c$ , $(\sqrt{c})^2$ is the same as $c$ because the square root and the square cancel each other out. $\newline$ Calculation: $(\sqrt{c})^2 = c$ .

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