Question 140490
 Perform the indicated operations:
2√[48] + 7√[12] –√[27]
:
Factor the values inside the radicals to reveal the perfect squares:
{{{2sqrt(16*3)}}} + {{{7sqrt(4*3)}}} - {{{sqrt(9*3)}}}
Extract the square root of those perfect squares:
{{{2*4sqrt(3)}}} + {{{7*2sqrt(3)}}} - {{{3sqrt(3)}}}
which is:
{{{8sqrt(3)}}} + {{{14sqrt(3)}}} - {{{3sqrt(3)}}}
These are like terms, just do the math and you have:
{{{19sqrt(3)}}}
:
:
Rationalize the denominator:
___ 2____
√[3] + √[2]
:
{{{2/(sqrt(3)+sqrt(2))}}}
multiply equation by the conjugate of the denominator: (any expression over itself = 1)
{{{2/(sqrt(3)+sqrt(2))}}} * {{{(sqrt(3)-sqrt(2))/(sqrt(3)-sqrt(2))}}} = {{{(2sqrt(3)-2sqrt(2))/(3 - 2)}}} = {{{(2sqrt(3)-2sqrt(2))/1}}} = {{{2sqrt(3)-2sqrt(2)}}}
:
Note that the when you FOIL the denominators, the middle terms cancel!