Question

1. (7 + √3)(7-√3)

2. (6+3√2)(5-√2)

3. 4√125

Answer 1

ok , you need to know this first:
\[\LARGE (a\pm b)(c\pm d)=ac\pm ad \pm bc \pm bd\]
I hope that' not too confusing..
In your case you have:
\[\Large (7+\sqrt3)(7-\sqrt3)=7\cdot 7-7\sqrt3 +\sqrt3\cdot 7-\sqrt3\cdot \sqrt3 \]
now what can you simplify there? :)
(question nr. 1)

Answer 2

\[\Large \Large (7+\sqrt3)(7-\sqrt3)=7\cdot 7\cancel{-7\sqrt3} \cancel{+\sqrt3\cdot 7}-\sqrt3\cdot \sqrt3 \]

Answer 3

what has left? :)

Answer 4

@joemost still there ? :)

Answer 5

the first one is:
\[\LARGE (7+\sqrt3)(7-\sqrt3)=7^2-(\sqrt3\;)^2=49-3=46\]
the second one..
\[\Large (6+3\sqrt2)(5-\sqrt2)=30-6\sqrt2+15\sqrt2-3\cdot 2\]
\[\Large =24+9\sqrt2\]
third one...
\[\LARGE 4\sqrt{125}=4\sqrt{5^2\cdot 5 }=4\sqrt{5^2}\cdot \sqrt5 \]
finish it...

Answer 6

ahh thanks, i got it :D

Answer 7

My Pleasure xD