Example Question - consecutive integers
Here are examples of questions we've helped users solve.
Finding Consecutive Whole Numbers for a Square Root Inequality
The image contains an inequality with a square root expression and two boxes. The inequality shows a square root of 83 \(\sqrt{83}\), and you are asked to find two consecutive whole numbers between which this value lies. To solve this, note that the value will be between the square roots of perfect squares that are closest to 83 but on either side of it. Since \(9^2 = 81\) and \(10^2 = 100\), \(\sqrt{83}\) will lie between 9 and 10. Hence, the solution to the inequality is: 9 < \(\sqrt{83}\) < 10 So, the two boxes should be filled with 9 and 10, respectively.
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.
Solving Inequality Involving Square Root of 141
The image shows an inequality that needs to be solved involving the square root of 141. The square root of 141 (√141) is a positive value because the square root of a positive number is also positive. To solve the inequality, we need to find two consecutive integers between which this square root value lies. The number 141 is not a perfect square, but we know that \( 12^2 = 144 \) and \( 11^2 = 121 \). Since 141 lies between 121 and 144, the square root of 141 must lie between 11 and 12. Since we're looking for integers, the two boxes in the inequality should contain the consecutive integers on either side of √141. Hence, the inequality can be written as: \[ 11 < \sqrt{141} < 12 \] This is the completed inequality statement with the integers placed accordingly.
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