Question

(square root 91 - 5square root 77)squared

Answer 1

To simplify the expression \((\sqrt{91} - 5\sqrt{77})^2\), we can use the formula for the square of a binomial:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

In this case, let \(a = \sqrt{91}\) and \(b = 5\sqrt{77}\).

1. Calculate \(a^2\):
\[
a^2 = (\sqrt{91})^2 = 91
\]

2. Calculate \(b^2\):
\[
b^2 = (5\sqrt{77})^2 = 25 \cdot 77 = 1925
\]

3. Calculate \(2ab\):
\[
2ab = 2 \cdot \sqrt{91} \cdot 5\sqrt{77} = 10\sqrt{91 \cdot 77}
\]

Now calculate \(91 \cdot 77\):
\[
91 \cdot 77 = 7007
\]

Therefore, \(2ab = 10\sqrt{7007}\).

4. Now substitute these values back into the binomial formula:
\[
(\sqrt{91} - 5\sqrt{77})^2 = a^2 - 2ab + b^2 = 91 - 10\sqrt{7007} + 1925
\]

5. Combine the constant terms:
\[
91 + 1925 = 2016
\]

Thus, the expression simplifies to:

\[
2016 - 10\sqrt{7007}
\]

So, the final answer is:

\[
\boxed{2016 - 10\sqrt{7007}}
\]