Sure! Let's solve the equation step by step.
We are given the equation:
[tex]\[ 211^2 + \square = 213^2 \][/tex]
Let’s calculate each part individually:
1. First, compute the square of 211:
[tex]\[ 211^2 = 44521 \][/tex]
2. Next, compute the square of 213:
[tex]\[ 213^2 = 45369 \][/tex]
3. We need to find the value of the unknown that makes the equation true. Let’s denote this unknown value as [tex]\( x \)[/tex]. Thus, we can write the equation as:
[tex]\[ 44521 + x = 45369 \][/tex]
4. To solve for [tex]\( x \)[/tex], we rearrange the equation to isolate [tex]\( x \)[/tex]:
[tex]\[ x = 45369 - 44521 \][/tex]
5. Now, perform the subtraction:
[tex]\[ x = 45369 - 44521 = 848 \][/tex]
So, the value that makes the equation [tex]\( 211^2 + \square = 213^2 \)[/tex] true is:
[tex]\[ \boxed{848} \][/tex]
