Question 74302
{{{(sqrt(3)+5)(sqrt(3)-3)}}}
{{{sqrt(3)*sqrt(3)-3*sqrt(3)+5*sqrt(3)-15}}}
{{{3-3*sqrt(3)+5*sqrt(3)-15}}}Since {{{sqrt(3)*sqrt(3)}}} is the same as {{{(sqrt(3))^2}}} we can say that {{{sqrt(3)*sqrt(3)=3}}}
{{{3+(-3+5)*sqrt(3)-15}}}Add like terms. In this case {{{sqrt(3)}}} is the common term. If we let{{{x=sqrt(3)}}} the it looks like {{{-3x+5x=(-3+5)x=2x}}}
{{{3+2*sqrt(3)-15}}}Finally add -15 to 3
{{{2*sqrt(3)-12}}}There's your simplified answer
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Check:
{{{(sqrt(3)+5)(sqrt(3)-3)}}}Numerically evaluate the given expression
{{{(1.73+5)(1.73-3)}}}
{{{(6.73)(-1.268)}}}
{{{-8.536}}}
{{{2*sqrt(3)-12}}}
{{{2(1.73)-12}}}
{{{3.464-12}}}
{{{-8.536}}}This shows that our simplified answer works.