Let's solve the equation [tex]\(\sqrt{a+5} = 4\)[/tex] step-by-step.
### Step 1: Isolate the Square Root
The given equation is:
[tex]\[
\sqrt{a+5} = 4
\][/tex]
### Step 2: Remove the Square Root
To remove the square root, we square both sides of the equation:
[tex]\[
(\sqrt{a+5})^2 = 4^2
\][/tex]
### Step 3: Simplify Both Sides
Squaring the square root on the left side cancels the square root, and squaring 4 gives 16:
[tex]\[
a + 5 = 16
\][/tex]
### Step 4: Solve for [tex]\(a\)[/tex]
To isolate [tex]\(a\)[/tex], subtract 5 from both sides of the equation:
[tex]\[
a + 5 - 5 = 16 - 5
\][/tex]
[tex]\[
a = 11
\][/tex]
### Step 5: Check the Solution
We should always check our solution by substituting the value back into the original equation to ensure it is correct.
Start with the original equation:
[tex]\[
\sqrt{a+5} = 4
\][/tex]
Substitute [tex]\(a = 11\)[/tex] back into the equation:
[tex]\[
\sqrt{11+5} = 4
\][/tex]
[tex]\[
\sqrt{16} = 4
\][/tex]
Since [tex]\(\sqrt{16} = 4\)[/tex] is a true statement, our solution is correct.
### Conclusion
The solution to the equation [tex]\(\sqrt{a+5} = 4\)[/tex] is:
[tex]\[
a = 11
\][/tex]
