Question

[sqrt(5)+sqrt(11)] [sqrt(5)-sqrt(11)]

Answer 1

So where are you having difficulties? Do you know how to distribute, AKA FOIL?

Answer 2

not with square roots

Answer 3

Look. It's like the product of some and difference.

Answer 4

It's exactly the same. Just being a square root doesn't make it not a number. You just foil as you did before.

Answer 5

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

Answer 6

@Yttrium I think showing him a shortcut is a bad idea when he is simply trying to learn the concept to begin with. Maybe once he gets comfortable with distributing that's a good next step.

Answer 7

so qould i get sqrt 25 - sqrt 121

Answer 8

Yep. Simplify sqrt25 - sqrt 121

Answer 9

so then just 5-11

Answer 10

then what?

Answer 11

\[(\sqrt{5}+\sqrt{11})(\sqrt{5}-\sqrt{11}) = \sqrt{5}*\sqrt{5} - \sqrt{5}*\sqrt{11}+\sqrt{11}*\sqrt{5} -\sqrt{11}*\sqrt{11}\]\[=5-\sqrt{5}\sqrt{11}+\sqrt{11}\sqrt{5} - 11\]\[=5-\sqrt{5}\sqrt{11}+\sqrt{5}\sqrt{11}-11\]\[=5-11+\sqrt{5}\sqrt{11}-\sqrt{5}\sqrt{11}\] = -6 + 0 = -6

Answer 12

I would do it with the difference of squares approach, but if you have a lot of radical signs (like in this problem), often it is easier to replace the quantities with letters, do the algebra like @Yttrium suggested, and then substitute the quantities back in.

\[(\sqrt{5} + \sqrt{11})(\sqrt{5}-\sqrt{11})\]Let \(a = \sqrt{5}\) and \(b = \sqrt{11}\) and then we have\[(a+b)(a-b)\]\[(a+b)(a-b) = a*a - a*b + a*b - b*b = a^2 - b^2\]Now substitute back:\[a^2-b^2 = (\sqrt{5})^2 - (\sqrt{11})^2\]but the square of the square root is just the original number, so that becomes \[5-11 = -6\]
just a lot easier than writing all of those @#%@#$ radical signs!