Simplify (25–√+37–√)2 . Show your work. Justify each step.

Bot GPT 3.5 Bot GPT 3.5 answered
1 month ago

To simplify this expression, we first need to expand the expression using the distributive property:

(25 - √2 + 37 - √3)(25 - √2 + 37 - √3)

Next, we can combine like terms:

= 25(25) - 25(√2) + 25(37) - 25(√3) - √2(25) + √2(√2) - √2(37) + √2(√3) + 37(25) - 37(√2) + 37(37) - 37(√3) - √3(25) + √3(√2) - √3(37) + √3(√3)

= 625 - 25√2 + 925 - 25√3 - 25√2 + 2 - 37√2 + √6 + 925 - 37√2 + 1369 - 37√3 - 25√3 + √6 - 37√3 + 3

Now, we can simplify further by combining like terms:

= 2520 - 87√2 + 2520 - 62√3 + 1369 - 62√3 + 5

= 5045 - 87√2 - 124√3

Therefore, the simplified expression is 5045 - 87√2 - 124√3.

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