Question 91333
{{{2sqrt(12)+4sqrt(27)}}}
Another way to write this is as follows:
{{{2sqrt(2^2*3)+4sqrt(3^2*3)}}}
Now, apply this property:
{{{sqrt(x^2)=x}}}
This gives you:
{{{2*2sqrt(3)+4*3sqrt(3)}}}
Simplifying:
{{{4sqrt(3)+12sqrt(3)}}}
Now that each term is the square root of the same thing, they can be combined:
{{{highlight(16sqrt(3))}}}
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{{{(sqrt(20)/5)-(1/sqrt(5))}}}
{{{(sqrt(2*2*5)/5)-(1/sqrt(5))}}}
Rationalize the denominator of the second term:
{{{(2sqrt(5)/5)-(sqrt(5)/5)}}}
Now perform the subtraction and you are done:
{{{highlight(sqrt(5)/5)}}}
Good Luck,
tutor_paul@yahoo.com