Calculate the square root of 2.
Understand the Problem
The question is asking to find the square root of 2, which is a mathematical calculation that determines a number that, when multiplied by itself, equals 2.
Answer
The square root of 2 is approximately $1.414$.
Answer for screen readers
The square root of 2 is approximately $1.414$.
Steps to Solve
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Identify the Square Root To find the square root of 2, we are looking for a number $x$ such that $x^2 = 2$.
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Approximation Method Since 2 is not a perfect square, we will need to use a numerical method such as estimation or a calculator to find an approximate value. We can start by estimating that the square root of 2 is between 1 and 2.
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Refine the Estimate We can further refine our estimate:
- Start by trying $1.4$: $$ 1.4^2 = 1.96 $$ So, it's slightly less than 2.
- Next, try $1.5$: $$ 1.5^2 = 2.25 $$ This is greater than 2.
- Continue Refining Keep narrowing down the range. Since $1.4^2 < 2 < 1.5^2$, we can try numbers between 1.4 and 1.5.
- Trying $1.42$: $$ 1.42^2 = 2.0164 $$
- Trying $1.41$: $$ 1.41^2 = 1.9881 $$
Now we see that $1.41^2 < 2 < 1.42^2$. We can narrow it further.
- Final Estimate Continuing this process gives us increasingly accurate estimates. The approximate square root of 2 is $1.414$.
The square root of 2 is approximately $1.414$.
More Information
The square root of 2 is an irrational number, which means it cannot be expressed as a simple fraction. Its decimal representation goes on forever without repeating.
Tips
- Forgetting that the square root can be irrational and assuming it must be a whole number.
- Not refining estimates closely enough, assuming that the first guess is the final answer.
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