To find the value of [tex]\(\sqrt{200.5^2 - 199.5^2}\)[/tex], we can use the algebraic identity for the difference of squares. The identity states that:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In our case, [tex]\(a = 200.5\)[/tex] and [tex]\(b = 199.5\)[/tex]. Let's apply the identity step by step:
1. Determine the difference [tex]\(a - b\)[/tex]:
[tex]\[
a - b = 200.5 - 199.5 = 1
\][/tex]
2. Determine the sum [tex]\(a + b\)[/tex]:
[tex]\[
a + b = 200.5 + 199.5 = 400
\][/tex]
3. Apply the difference of squares identity:
[tex]\[
200.5^2 - 199.5^2 = (200.5 - 199.5)(200.5 + 199.5) = 1 \times 400 = 400
\][/tex]
4. Calculate the square root of the result:
[tex]\[
\sqrt{200.5^2 - 199.5^2} = \sqrt{400} = 20
\][/tex]
Thus, the value of [tex]\(\sqrt{200.5^2 - 199.5^2}\)[/tex] is 20.
