What is the value of the square root of 2?
Understand the Problem
The question is asking for the value of the square root of 2, which is a mathematical constant. The square root of 2 is an irrational number approximately equal to 1.41421356237.
Answer
The value of the square root of 2 is approximately $1.41421356237$.
Answer for screen readers
The value of the square root of 2 is approximately $1.41421356237$.
Steps to Solve
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Understanding the square root of a number The square root of a number $x$ is a value $y$ such that when $y$ is multiplied by itself, it gives $x$. This can be expressed as $y^2 = x$. In this case, we want to find the square root of $2$.
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Calculating the approximate value The square root of $2$ cannot be expressed as a simple fraction, so we use approximation methods like long division or a calculator to find an accurate value.
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Using a calculator By inputting $\sqrt{2}$ into a calculator, we find that the approximate value is about $1.41421356237$.
The value of the square root of 2 is approximately $1.41421356237$.
More Information
The square root of $2$ is known as the first irrational number discovered, which means it cannot be expressed as a fraction of two integers. It is commonly used in geometry, particularly in the context of diagonal lengths in squares.
Tips
- Confusing the square root symbol with absolute value, which can lead to incorrect results.
- Underestimating the irrational nature of $\sqrt{2}$ and assuming it can be precisely expressed as a ratio of integers.
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