Simplify (25–√+37–√)2
. Show your work. Justify each step.
First, let's simplify the expressions under the square roots:
25 - √37 - √37 = 25 - 2√37
Now, we have (25 - 2√37)^2. To expand this expression, we can use the formula (a - b)^2 = a^2 - 2ab + b^2.
So, for this case:
a = 25
b = √37
(25 - 2√37)^2 = 25^2 - 2(25)(2√37) + (2√37)^2
= 625 - 100√37 + 4(37)
= 625 - 100√37 + 148
= 773 - 100√37
Therefore, (25 - √37 - √37)^2 simplifies to 773 - 100√37.