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Simplify (25–√+37–√)2
. Show your work. Justify each step.
To simplify (25 - √2 + 37 - √2)^2, we first need to simplify the expression inside the parentheses.
25 - √2 + 37 - √2
= 62 - 2√2
Now we square this simplified expression:
(62 - 2√2)^2
= (62 - 2√2)(62 - 2√2)
= 62*62 - 2*62*2√2 - 2√2*62 + 2√2*2√2
= 3844 - 248√2 - 248√2 + 8*2
= 3844 - 496√2 + 32
= 3876 - 496√2
Therefore, (25 - √2 + 37 - √2)^2 simplifies to 3876 - 496√2.