Question - Solving Inequality Involving Square Root of 141
mathinequality involving square rootsolving square root inequalitysquare root of 141consecutive integers
Solution:
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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