What number times itself equals 10?
Understand the Problem
The question is asking us to find a number that, when multiplied by itself, equals 10. This involves solving for a square root problem.
Answer
$x = \sqrt{10}, x = -\sqrt{10}$
Answer for screen readers
The solutions to the equation are $x = \sqrt{10}$ and $x = -\sqrt{10}$.
Steps to Solve
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Identify the equation to solve We start with the equation we need to solve: $$ x^2 = 10 $$
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Take the square root of both sides To isolate $x$, we take the square root of both sides of the equation: $$ x = \pm \sqrt{10} $$
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Simplify the square root The square root of 10 cannot be simplified further, so the values of $x$ are: $$ x = \sqrt{10} \quad \text{or} \quad x = -\sqrt{10} $$
The solutions to the equation are $x = \sqrt{10}$ and $x = -\sqrt{10}$.
More Information
The square root of 10 is approximately 3.162. This means the number you are looking for, when squared, gives you 10. Therefore, both positive and negative values of the square root are valid solutions since both will result in the same squared value.
Tips
- Forgetting to include both the positive and negative roots when taking the square root.
- Confusing the square root operation with squaring, leading to the wrong equation setup.
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