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Sagot :
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]
### 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]
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