+118702 √49−20√6=√25+24−20√6This might be helpful because 25 is a square and 24 is a multiple of 6=√25−20√6+4∗6=√52−20√6+(2√6)2=√52−2∗5∗2√6+(2√6)2=√(5−2√6)2=|5−2√6|=5−2√6
Now maybe you can attempt the second one.
Start by factoring out the 2.
+4625 1. I'll just try this problem...I don't know if I'll get it !
Let √49−20√6=a−b.
We can square both sides to get, 49−20√6=(a−b)2.
Expanding this, gives us 49−20√6=a2+b2−2ab.
Now, by a bit of matching, we can see that a2−b2=49 and −2ab=−20√6 (Same thing as 2ab=20√6)
This might be a bit of tedious work, but by a bit of inspection a=5 and b=2√6 work.
Thus, the answer is a−b=5−2√6.
+118702 Hi Tertre,
I've only learnt this recently and I do not do it quite like that. My technique is pretty bad.
But your way looks really good.
Most times I do not think it would work. I mean i doubt that questions like this can be simplified all that often.
If the questions says 'simplify' it is a reasonable to assume that it can be done in that instance.
