Example Question - square root of 141
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.
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.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com