Type the correct answer in the box. Use numerals instead of words.

Consider this expression:
[tex]\[ \left|m^2 + n^2\right| \][/tex]

When [tex]\( m = -5 \)[/tex] and [tex]\( n = 3 \)[/tex], the value of the expression is [tex]\(\square\)[/tex]



Answer :

To find the value of the expression [tex]\(\left|m^2 + n^2\right|\)[/tex] when [tex]\(m = -5\)[/tex] and [tex]\(n = 3\)[/tex], follow these steps:

1. Calculate [tex]\(m^2\)[/tex]:
[tex]\[ m = -5 \][/tex]
[tex]\[ m^2 = (-5)^2 = 25 \][/tex]

2. Calculate [tex]\(n^2\)[/tex]:
[tex]\[ n = 3 \][/tex]
[tex]\[ n^2 = 3^2 = 9 \][/tex]

3. Sum [tex]\(m^2\)[/tex] and [tex]\(n^2\)[/tex]:
[tex]\[ 25 + 9 = 34 \][/tex]

4. Calculate the absolute value of the sum:
[tex]\[ \left|34\right| = 34 \][/tex]

Therefore, the value of the expression [tex]\(\left|m^2 + n^2\right|\)[/tex] is [tex]\( \boxed{34} \)[/tex].