simplify the expression | squaroot 6 - 6 |

To simplify the expression \( \left| \sqrt{6} - 6 \right| \), follow these steps:

1. Calculate the approximate value of \( \sqrt{6} \):
   \[
   \sqrt{6} \approx 2.449
   \]

2. Subtract 6 from \( \sqrt{6} \):
   \[
   2.449 - 6 = -3.551
   \]

3. Since this result is negative, apply the absolute value:
   \[
   \left| -3.551 \right| = 3.551
   \]

Thus, the simplified expression is approximately:

\[
\left| \sqrt{6} - 6 \right| \approx 3.551
\]

Would you like more details on any part of this process? Here are five related questions for further exploration:

1. How do you calculate square roots of non-perfect squares manually?
2. Why does the absolute value turn a negative number into a positive one?
3. Can you simplify the expression without approximating the square root?
4. How would the expression change if it were \( \left| 6 - \sqrt{6} \right| \)?
5. What is the importance of absolute values in equations?

**Tip:** Always calculate the value inside the absolute sign before applying it.

This guide walks you through simplifying the expression | √6 - 6 |. It covers essential algebra concepts like square roots and absolute values. Learn how to handle non-perfect squares and apply absolute value in this problem, aimed at students in Grades 6-8.

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