SOLUTION: Please simply this radical expression. I got stuck. {{{sqrt(3/4) + sqrt(12)}}} thank you

Algebra ->  Radicals -> SOLUTION: Please simply this radical expression. I got stuck. {{{sqrt(3/4) + sqrt(12)}}} thank you      Log On


   



Question 213198: Please simply this radical expression. I got stuck.

sqrt%283%2F4%29+%2B+sqrt%2812%29

thank you

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%283%2F4%29+%2B+sqrt%2812%29

Write the first term as the quotient of two square roots

sqrt%283%29%2Fsqrt%284%29+%2B+sqrt%2812%29

Replace sqrt%284%29 by 2

sqrt%283%29%2F2+%2B+sqrt%2812%29

Now break 12 into 4%2A3

sqrt%283%29%2F2+%2B+sqrt%284%2A3%29

Write the second term as the product of two square roots

sqrt%283%29%2F2+%2B+sqrt%284%29sqrt%283%29

Replace sqrt%284%29 by 2

sqrt%283%29%2F2+%2B+2sqrt%283%29

Put 1 under the second term:

sqrt%283%29%2F2+%2B+%282%2Asqrt%283%29%29%2F1

Get LCD of 2 and multiply top and bottom by 2:

sqrt%283%29%2F2+%2B+%282%2Asqrt%283%29%2A2%29%2F%281%2A2%29

sqrt%283%29%2F2+%2B+%284%2Asqrt%283%29%29%2F2 

Write as one fraction:

%28sqrt%283%29+%2B4%2Asqrt%283%29%29%2F2

Put 1%2A%22%22 in front of the first term:

%281%2Asqrt%283%29+%2B4%2Asqrt%283%29%29%2F2

Combine like terms

%285sqrt%283%29%29%2F2

Edwin