How would you solve for:
(the square root of 7-the square root of 3)^2
^=the power of
[sqrt(7) - sqrt(3)]^2 =
7 + 3 - 2sqrt(21) = 10 - 2sqrt(21)
To solve for (the square root of 7 - the square root of 3) squared, you can follow these steps:
1. Start with the expression (sqrt(7) - sqrt(3))^2.
2. Apply the rule of expanding a binomial squared, which states that (a - b)^2 = a^2 - 2ab + b^2.
3. In this case, let a = sqrt(7) and b = sqrt(3). Substituting these values into the formula, we get (sqrt(7))^2 - 2(sqrt(7))(sqrt(3)) + (sqrt(3))^2.
4. Simplify each term: sqrt(7)^2 = 7, sqrt(3)^2 = 3.
5. Multiply the middle term: 2(sqrt(7))(sqrt(3)) = 2sqrt(21).
6. Combine the simplified terms: 7 - 2sqrt(21) + 3.
7. Simplify further: 10 - 2sqrt(21).
Therefore, (the square root of 7 - the square root of 3)^2 equals 10 - 2sqrt(21).