Answer :

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.