Example Question - inequality involving square root
Here are examples of questions we've helped users solve.
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.
Inequality Involving Square Root of 10
The image shows an inequality involving a square root, specifically the square root of 10. The inequality symbols, "<", suggest that we need to find two numbers where the negative square root of 10 lies in between. The square root of 10 is an irrational number, but we can approximate its value for this purpose. The square root of 10 is approximately equal to 3.16 (rounded to two decimal places). The negative square root of 10 would be approximately -3.16. Based on this, we can deduce that -4 is less than -√10, and -√10 is less than -3, because -4 < -3.16 < -3. So the two blank boxes should contain numbers according to this rule. Therefore, the inequality can be filled as: -4 < -√10 < -3 It appears that the intent of the image was to place numbers in the blank boxes to demonstrate understanding of the order of these numbers. The numbers -4 and -3 are likely candidates to solve this particular problem.
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