Question

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

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Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify (25–√+37–√)^2, we first expand the expression using the distributive property of exponents.

(25–√+37–√)^2 = (25–√+37–√)(25–√+37–√)

Next, we multiply each term in the first parentheses by each term in the second parentheses using the distributive property.

(25–√)(25–√) + (25–√)(37–√) + (37–√)(25–√) + (37–√)(37–√)

Now, we simplify each product by multiplying the terms.

(625 - 50√ + √^2) + (925 - 25√ + 37√ - √^2) + (925 - 25√ + 37√ - √^2) + (1369 - 74√ + √^2)

Simplifying further, we get

625 - 50√ + 25 + 925 - 25√ + 37√ - 37 + 925 - 25√ + 37√ - 25 + 1369 - 74√ + 37

Combine like terms:

(625 + 25 + 925 - 37 + 925 - 25 - 25 + 1369) + (-50√ - 25√ + 37√ - 25√ - 74√)

Now, simplify:

(2941) + (-63√)

Therefore, the simplified form of (25–√+37–√)^2 is 2941 - 63√.