Answer :

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].