What is (5 -(sqrt)2) (3 + sqrt 2)?

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Answer 1 · 2015-09-18T09:32:49

#13+2sqrt2#

First we must expand the equation of #(5 -sqrt 2) (3 + sqrt 2)#. And we will get the equation be like;

#(5 -sqrt 2) (3 + sqrt 2)#

#=5(3)+5(sqrt2)-3(sqrt2)-sqrt2(sqrt2)#

Note that for #sqrt2(sqrt2)#, we can calculate it by;

#=sqrt2xxsqrt2= (2)^(1/2)xx(2)^(1/2)= 2^(1/2+1/2)= 2^1 =2#

And we will get;

#=15+5sqrt2-3sqrt2-2#

#5sqrt2# can subtract #3sqrt2# since it has the same base, which is #sqrt2#. Calculate all of it and we will get;

#=13+2sqrt2#