To simplify the expression
[tex]\[ \sqrt{(5-7)^2 + (8-3)^2} \][/tex]
we will proceed step-by-step through the calculations:
1. Calculate the value inside each set of parentheses:
- For [tex]\((5 - 7)\)[/tex]:
[tex]\[
5 - 7 = -2
\][/tex]
- For [tex]\((8 - 3)\)[/tex]:
[tex]\[
8 - 3 = 5
\][/tex]
2. Square the results of each calculation:
- For [tex]\((-2)^2\)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
- For [tex]\(5^2\)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
3. Add the squared results together:
[tex]\[
4 + 25 = 29
\][/tex]
4. Take the square root of the sum:
[tex]\[
\sqrt{29} \approx 5.385
\][/tex]
Therefore, the expression simplifies to [tex]\( \sqrt{29} \approx 5.385 \)[/tex].
