Example Question - irrational number
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.
Solving Inequality with Square Root of 5
It looks like the image you've provided contains an inequality with two blank boxes and the square root of 5. It's difficult to determine specifically what is being asked because there's no context or additional instructions. However, I can give you a general idea of what the inequality suggests. The square root of 5 is an irrational number, approximately equal to 2.236. An inequality featuring the square root of 5 between two boxes might be asking for you to identify two integers, one that is less than the square root of 5, and one that is greater. Given this, the answers could be: - The integer less than √5: 2 - The integer greater than √5: 3 Therefore, the completed inequality with the integers in place would be: 2 < √5 < 3 These integers are the largest whole number less than √5 and the smallest whole number greater than √5, respectively.
Finding Integers for Square Root of 141
This problem involves finding the two integers that the square root of 141 lies between. The square root of 141 is an irrational number because 141 is not a perfect square; thus, it cannot be expressed as an exact integer. To solve this question, we need to find the two perfect squares nearest to 141, one that is less than 141 and one that is greater than 141. The perfect square closest to 141 but less than 141 is 121, because \( \sqrt{121} = 11 \). The next perfect square greater than 141 is 144, because \( \sqrt{144} = 12 \). Therefore, the square root of 141 is greater than 11 but less than 12. Putting this into the inequality given in the image: 11 < \( \sqrt{141} \) < 12 So the boxes in the inequality would be filled in with 11 and 12, accordingly.
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