How do you simplify #( 7 - sqrt7)/(10 +sqrt3)#?

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Answer 1 · 2017-12-08T15:39:46

There is not much you can do. Only put square root to the top.

#(7−√7)/(10+√3)*(10-sqrt(3))/(10-sqrt(3))=#

#=(70-10sqrt(7)+sqrt(21)-7sqrt(3))/(10^2-(sqrt(3))^2)=#

#=(70-10sqrt(7)+sqrt(21)-7sqrt(3))/97#

Answer 2 · 2017-12-08T15:43:53

#=(70-7sqrt3-10sqrt7+sqrt21)/97#

To simplify this expression we rationalise the denominator. That is multiply top and bottom by a term that will remove the square root.

We make use of the difference of squares identity

#a^2-b^2=(a+b)(a-b)#

#(7-sqrt7)/(10+sqrt3)=(7-sqrt7)/(10+sqrt3)xx(10-sqrt3)/(10-sqrt3)#

#=(70-7sqrt3-10sqrt7+sqrt21)/(100-3)#

#=(70-7sqrt3-10sqrt7+sqrt21)/97#