What is the square root of 153?
Understand the Problem
The question is asking for the square root of the number 153. To solve this, we need to find a number that, when multiplied by itself, equals 153.
Answer
$$ \sqrt{153} \approx 12.369 $$
Answer for screen readers
$$ \sqrt{153} \approx 12.369 $$
Steps to Solve
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Identify the Square Root To find the square root of 153, we need to determine what number multiplied by itself gives 153. In mathematical terms, we are looking for $x$ such that $x^2 = 153$.
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Estimate the Square Root Since $12^2 = 144$ and $13^2 = 169$, we can estimate that the square root of 153 lies between 12 and 13.
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Use a Calculator or Approximation Technique To get a more precise answer, we can use a calculator or an approximation method like averaging. Using a calculator, we find: $$ \sqrt{153} \approx 12.369 $$
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Round the Answer if Necessary Depending on the requirements of your problem, you might want to round this answer. For example, rounded to two decimal places, it would be: $$ \sqrt{153} \approx 12.37 $$
$$ \sqrt{153} \approx 12.369 $$
More Information
The square root of a number represents a value that, when squared, results in that number. The square root of 153 is approximately 12.366, which is an irrational number, meaning it cannot be expressed exactly as a fraction and has a non-repeating decimal expansion.
Tips
- Forgetting to estimate the square root before calculating, which can lead to confusion about where the square root lies.
- Miscalculating the square root when using a calculator; it's important to ensure the calculator is in the correct mode, especially when dealing with fractions.
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