Question

(5+sqrt11)(5-sqrt11)

Answer 1

This is what is called a difference of two squares.

If you multiply
\[(a+b)(a-b) = a^2 - ab + ab - b^2\]\[a^2-b^2\]Hence the name "difference of squares"

This is a very useful pattern to recognize. With it, you can immediately recognize that your problem is a difference of squares, with \(a = 5,~b=\sqrt{11}\) which means you can write the answer as
\[5^2 - (\sqrt{11})^2\]but of course squaring a square root removes the radical sign and leaves the quantity underneath it, so that becomes
\[5^2-11 = 25-11 = 14\]

Or, if you prefer:
\[(5+\sqrt{11})(5-\sqrt{11}) = 5*5 - 5\sqrt{11} + 5\sqrt{11} - \sqrt{11}*\sqrt{11}\]\[=25-11 = 14\]

Answer 2

25-11

Answer 3

thanks that helps alot:)