Answer :
We are given the equation
[tex]$$
r^2 = 6.25.
$$[/tex]
To solve for [tex]$r$[/tex], follow these steps:
1. Recognize that if [tex]$r^2 = 6.25$[/tex], then [tex]$r$[/tex] must be a number whose square is [tex]$6.25$[/tex].
2. To isolate [tex]$r$[/tex], take the square root of both sides of the equation. Remember that taking the square root of a squared variable gives the absolute value of that variable. That is,
[tex]$$
|r| = \sqrt{6.25}.
$$[/tex]
3. Since the square root of [tex]$6.25$[/tex] is [tex]$2.5$[/tex], this tells us that
[tex]$$
|r| = 2.5.
$$[/tex]
4. The absolute value equation [tex]$|r| = 2.5$[/tex] has two solutions:
[tex]$$
r = 2.5 \quad \text{or} \quad r = -2.5.
$$[/tex]
Thus, the solutions to the equation are
[tex]$$
r = 2.5 \quad \text{and} \quad r = -2.5.
$$[/tex]
[tex]$$
r^2 = 6.25.
$$[/tex]
To solve for [tex]$r$[/tex], follow these steps:
1. Recognize that if [tex]$r^2 = 6.25$[/tex], then [tex]$r$[/tex] must be a number whose square is [tex]$6.25$[/tex].
2. To isolate [tex]$r$[/tex], take the square root of both sides of the equation. Remember that taking the square root of a squared variable gives the absolute value of that variable. That is,
[tex]$$
|r| = \sqrt{6.25}.
$$[/tex]
3. Since the square root of [tex]$6.25$[/tex] is [tex]$2.5$[/tex], this tells us that
[tex]$$
|r| = 2.5.
$$[/tex]
4. The absolute value equation [tex]$|r| = 2.5$[/tex] has two solutions:
[tex]$$
r = 2.5 \quad \text{or} \quad r = -2.5.
$$[/tex]
Thus, the solutions to the equation are
[tex]$$
r = 2.5 \quad \text{and} \quad r = -2.5.
$$[/tex]
