Sqrt(97+56*sqrt(3))/sqrt(7+4*sqrt(3))*sqrt(7-4sqrt(3))

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вопрос

To simplify the given expression, we first see that we can combine the last two square roots by using the difference of squares formula: (a - b)(a + b) = a^2 - b^2.

So, sqrt(7 + 4√3) * sqrt(7 - 4√3) = sqrt((7)^2 - (4√3)^2) = sqrt(49 - 48) = sqrt(1) = 1.

Now, the expression becomes:

sqrt(97 + 56√3) / sqrt(7 + 4√3) * 1

Since we are only multiplying by 1, the expression remains unchanged. Therefore, the simplified version of the expression is:

sqrt(97 + 56√3) / sqrt(7 + 4√3)