Question - Completing a Mathematical Inequality with Square Root
Solution:
The image shows an incomplete mathematical inequality with a square root. We see $$ \sqrt{68} $$ and two blank spaces, one to the left and one to the right of this square root, waiting to be filled with appropriate numbers to complete the inequality.To find numbers that fit this inequality, we first need to estimate the value of $$ \sqrt{68} $$. Since $$ 8^2 = 64 $$ and $$ 9^2 = 81 $$, we know that $$ \sqrt{68} $$ falls between 8 and 9. More precisely, since 68 is closer to 64 than it is to 81, $$ \sqrt{68} $$ will be closer to 8 than to 9.Therefore, to satisfy the inequality, we can choose a number less than 8 for the blank on the left (for example, 7) and a number between 8 and 9 for the blank on the right (such as 8.5).So, one possible way to fill the blanks would be:\[ 7 < \sqrt{68} < 8.5 \]Note that these are just example numbers. Any number less than 8 could fit into the first blank, and any number between 8 and 9 (but not including 9) could fit into the second blank.
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