SOLUTION: perform and simplify completely. {{{ (sqrt(6)+ 3sqrt(3))}}}^2 would the correct answer be 6+ 3sqrt(9)

Algebra ->  Square-cubic-other-roots -> SOLUTION: perform and simplify completely. {{{ (sqrt(6)+ 3sqrt(3))}}}^2 would the correct answer be 6+ 3sqrt(9)      Log On


   



Question 621717: perform and simplify completely.
+%28sqrt%286%29%2B+3sqrt%283%29%29^2

would the correct answer be 6+ 3sqrt(9)

Found 3 solutions by ewatrrr, tutor_paul, josmiceli:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,
+%28sqrt%286%29%2B+3sqrt%283%29%29^2
+%28sqrt%286%29%2B+3sqrt%283%29%29%28sqrt%286%29%2B+3sqrt%283%29%29
F First terms 6
O Outside terms 3sqrt%2818%29=+3sqrt%289%2A2%29+=+9sqrt%282%29
I Inside terms 3sqrt%2818%29=+3sqrt%289%2A2%29+=+9sqrt%282%29
L Last terms 27
+%28sqrt%286%29%2B+3sqrt%283%29%29^2 = 33 + 18sqrt(2)

Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%286%29%2B+3sqrt%283%29%29%5E2
============================
Follow the rules for squaring a binomial:
1. Square first term
2. Multiply the 2 terms and double the result add to above
3. Square 2nd term add the result to above
----------------------------
When you follow these rules, you get:
6%2B%282%29%283%29sqrt%286%29sqrt%283%29%2B%289%29%283%29
Simplify:
6%2B6sqrt%2818%29%2B27
33%2B6sqrt%2818%29
Simplify the radical:
highlight%2833%2B18sqrt%282%29%29
====================
Good Luck,
tutor_paul@yahoo.com

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%28sqrt%286%29+%2B+3%2Asqrt%283%29%29+%5E2+

+6+%2B+6%2Asqrt%2818%29+%2B+9%2A3+
+27+%2B+6+%2B+6%2Asqrt%28+9%2A2+%29+
+33+%2B+6%2Asqrt%289%29%2Asqrt%282%29+
+33+%2B+6%2A3%2Asqrt%282%29+
+33+%2B+18%2Asqrt%282%29+ answer
----------------
I can check this using a calculator
for the square roots
+sqrt%286%29+=+2.4495+
+sqrt%283%29+=+1.7321+
+sqrt%282%29+=+1.4142+
and
+%28sqrt%286%29+%2B+3%2Asqrt%283%29%29+=+2.4495+%2B+3%2A1.7321+
++2.4495+%2B+3%2A1.7321+=+2.4495+%2B+5.1963+
++2.4495+%2B+5.1963+=+7.6458+
+7.6458%5E2+=+58.4583+
and
+33+%2B+18%2Asqrt%282%29+=+33+%2B+18%2A1.4142+
+33+%2B+18%2A1.4142+=+33+%2B+25.4558+
+33+%2B+25.4558+=+58.4558+
The answers look close enough