Question - Solving Inequality with Negative Square Root
Solution:
The image shows an inequality with a square root and two empty boxes for numbers. The inequality is as follows:\[ \text{[Box 1]} < -\sqrt{118} < \text{[Box 2]} \]To solve this, let's find the square root of $$ 118 $$:The square root of $$ 118 $$ is an irrational number, and it is approximately equal to $$ 10.86278 $$ when we take the positive root. However, in this context, we're looking at the negative square root of $$ 118 $$, which would be approximately $$ -10.86278 $$. Now, we're looking for two integers that the negative square root of $$ 118 $$ falls between. Since $$ -10.86278 $$ is between $$ -11 $$ and $$ -10 $$, these would be the integers we are looking for:\[ -11 < -\sqrt{118} < -10 \]So, the numbers that should fill the boxes from left to right are $$ -11 $$ and $$ -10 $$.
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