Question 422841
I do not fully understand radical expressions like 7 times the square root of 12.
Taking your example {{{7sqrt(12)}}}
Factor 12 in a way the reveals at perfect square
{{{7sqrt(4*3)}}}
Extract the square root of 4, which is 2
{{{7*2sqrt(3)}}} = {{{14sqrt(3)}}}, no further action can be taken
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Check this on a calc: enter 7*{{{sqrt(12)}}} to get 24.2487..
Then enter your solution: 14*{{{sqrt(3)}}} to get 24.2487.., the same if you did it right.
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Also how do you add and subtract them to get answers with a number outside a square root like 6 times the square root of 54 or something.
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You can add and subtract only like terms,  For example {{{3sqrt(2)}}} + {{{2sqrt(2)}}} = {{{5sqrt(2)}}}
but {{{3sqrt(2)}}} + {{{2sqrt(3)}}} are not like terms and can't be added
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However, after simplifying they may be like terms, this example
{{{2sqrt(6)}}} + {{{6sqrt(54)}}}
Factor 54 to reveal a perfect square
{{{2sqrt(6)}}} + {{{6sqrt(9*6)}}}
Extract the square root of 9
{{{2sqrt(6)}}} + {{{6*3sqrt(6)}}} = {{{2sqrt(6)}}} + {{{18sqrt(6)}}} =
now they are like terms so we have: {{{20sqrt(6)}}}

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One more question. When there are letters and numbers with the variable is it any different to solve. For example the square root of 128n^17 
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Using {{{sqrt(128n^17)}}} we can factor to reveal perfect squares
{{{sqrt(64*2*n^16*n)}}}
remember the sqrt of n^16 is n^8 (n^8*n^8), so we have
{{{8*n^8*sqrt(2n)}}}
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We treat variables the same way, just remember the law of exponents.