Solve for u, where u is a real number. √(u + 9) = 8
Understand the Problem
The question is asking to solve the equation √(u + 9) = 8 for the variable u, where u is specified to be a real number. This involves isolating u and performing algebraic steps to find its value.
Answer
The solution to the equation is $u = 55$.
Answer for screen readers
The value of $u$ is $55$.
Steps to Solve
-
Square both sides of the equation
To eliminate the square root, we square both sides of the equation:
$$ \left(\sqrt{u + 9}\right)^2 = 8^2 $$
This simplifies to:
$$ u + 9 = 64 $$ -
Isolate the variable u
Now, we isolate $u$ by subtracting 9 from both sides:
$$ u + 9 - 9 = 64 - 9 $$
This simplifies to:
$$ u = 55 $$
The value of $u$ is $55$.
More Information
The solution indicates that $u = 55$ satisfies the original equation. You can verify this by substituting back into the original equation:
$$ \sqrt{55 + 9} = \sqrt{64} = 8 $$.
Tips
- Not squaring both sides correctly: When squaring, ensure both sides are fully squared.
- Ignoring the domain of the square root: The expression inside the square root must be non-negative, but in this case, $55 + 9 = 64$ is okay.
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