Question 756370
{{{ ( sqrt(20) + sqrt(5) ) / sqrt(10) }}}
{{{ ( sqrt(4*5) + sqrt(5) ) / sqrt(2*5) }}}
{{{ ( sqrt(4)*sqrt(5) + sqrt(5) ) / ( sqrt(2)*sqrt(5) ) }}}
{{{ sqrt(5) * ( sqrt(4) + 1 ) / ( sqrt( 5 ) * sqrt( 2 )) }}}
Divide top and bottom by {{{ sqrt(5) }}}
{{{ ( 2 + 1 ) / sqrt(2) }}}
{{{ 3 / sqrt(2) }}}
Multiply top and bottom by {{{ sqrt(2) }}}
{{{ ( 3*sqrt(2) ) / 2 }}}
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You can actually check this with a calculator:
{{{ ( sqrt(20) + sqrt(5) ) / sqrt(10) = ( 4.4721 + 2.2361 ) / 3.1623 }}}
{{{  ( 4.4721 + 2.2361 ) / 3.1623 = 6.7082 / 3.1623 }}}
{{{ 6.7082 / 3.1623 = 2.1213 }}}
and
{{{ ( 3*sqrt(2) ) / 2 = ( 3*1.4142 ) / 2 }}}
{{{ 4.2426 / 2 = 2.1213 }}}
OK