Example Question - square root of 2
Here are examples of questions we've helped users solve.
Finding Numbers Related to Square Root of 2
The image displays two empty boxes separated by inequality signs with the square root of 2 in the middle, like so: \[ \Box < \sqrt{2} < \Box \] We are likely being asked to find two numbers that satisfy these inequalities, where one number is less than the square root of 2 and the other is greater. The square root of 2 is an irrational number which is approximately 1.414. So we need to find a number that is less than 1.414 and another that is greater. A simple solution is to use 1 for the first box and 2 for the second box, as 1 is less than the square root of 2 and 2 is greater than square root of 2. The resulting completed inequality would look like this: \[ 1 < \sqrt{2} < 2 \] This is a valid solution since 1 and 2 are integers that satisfy the inequalities on either side of the square root of 2.
Understanding Inequalities with Square Root of 2
The image shows two inequality signs surrounding the square root of 2 (√2), with blanks where numbers would be. To solve this problem, you need to find two numbers that are consecutive integers where the square root of 2 fits between them. The square root of 2 is approximately 1.414. It is more than 1 but less than 2. Therefore, the two integers that would fit on either side of √2 would be 1 and 2. The inequality then reads as: 1 < √2 < 2 This indicates that the square root of 2 is greater than 1 but less than 2.
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