How do you simplify $(5+ sqrt 6) (5-sqrt 2)$ ?

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Answer 1 · 2016-09-05T04:05:34

$25+5(sqrt6-sqrt2)-2sqrt3$ .

The Expression $=(5+sqrt6)(5-sqrt2)$

$=5(5-sqrt2)+(5-sqrt2)sqrt6$

$=25-5sqrt2+5sqrt6-sqrt2*sqrt6$

But, knowing that, $a^m*b^m=(ab)^m,$ we find,

$sqrt2*sqrt6=2^(1/2)*6^(1/2)=(2*6)^(1/2)=12^(1/2)=(2^2*3)^(1/2)$

$=(2^2)^(1/2)*3^(1/2)=2^(1/2*2)*3^(1/2)=2^1*3^(1/2)=2sqrt3$

Finally, the simplified expression reads

$25+5(sqrt6-sqrt2)-2sqrt3$ .

Enjoy Maths.!

How do you simplify (5+ sqrt 6) (5-sqrt 2)(5+ sqrt 6) (5-sqrt 2)?