Certainly! Let's solve the given problem step by step.
We are given the equation [tex]$(a + b) = k^2$[/tex] and we need to find the positive value of [tex]$k$[/tex].
### Step-by-Step Solution
1. Identify the Sum:
We are given values for [tex]$a$[/tex] and [tex]$b$[/tex]. In this case, let's assume:
[tex]\[
a = 4 \quad \text{and} \quad b = 5
\][/tex]
Now, compute the sum of [tex]$a$[/tex] and [tex]$b$[/tex]:
[tex]\[
a + b = 4 + 5 = 9
\][/tex]
2. Equation Setup:
From the equation we are working with:
[tex]\[
a + b = k^2
\][/tex]
Substitute the sum we calculated:
[tex]\[
9 = k^2
\][/tex]
3. Solving for [tex]$k$[/tex]:
To find the positive value of [tex]$k$[/tex], we need to solve the equation:
[tex]\[
k^2 = 9
\][/tex]
Taking the square root of both sides gives:
[tex]\[
k = \sqrt{9}
\][/tex]
4. Simplifying the Square Root:
The positive square root of 9 is:
[tex]\[
\sqrt{9} = 3
\][/tex]
5. Conclusion:
Thus, the positive value of [tex]$k$[/tex] is:
[tex]\[
k = 3
\][/tex]
So, the positive value of [tex]$k$[/tex] given that [tex]$(a + b) = k^2$[/tex] is [tex]$\boxed{3}$[/tex].
