Chapter A, Problem 45E

(a)

To determine

To explain: Whether the statement $\sqrt{16}=\pm 4$ is true or not and give an explanation.

(b)

To determine

To explain: Whether the statement $\sqrt{4^2}=\sqrt{{\left(-4\right)}^2}$ is true or not and give an explanation.

(c)

To determine

To explain: Whether the statement “the two real numbers that satisfy the condition $\left|x\right|=-2$” is true or not and give an explanation.

(d)

To determine

To explain: Whether the statement $\left|{\pi }^2-9\right|<0$ is true or not and give an explanation.

(e)

To determine

To explain: Whether the statement “the point $\left(1,1\right)$ is inside the circle of radius 1 centered at the origin” is true or not and give an explanation.

(f)

To determine

To explain: Whether the statement “ $\sqrt{x^4}=x^2$ for all real numbers x” is true or not and give an explanation.

(f)

To determine

To explain: Whether the statement “ $\sqrt{a^2}<\sqrt{b^2}$ implies $a<b$ for all real numbers a and b” is true or not and give an explanation.