SOLUTION: simplify the fractional expression: {{{ sqrt(1+(x^3 - 1/4x^3)^2)}}} This is the last question i have in this section an stumped on where to start. Tinking to start/: {{{ s

Algebra ->  Radicals -> SOLUTION: simplify the fractional expression: {{{ sqrt(1+(x^3 - 1/4x^3)^2)}}} This is the last question i have in this section an stumped on where to start. Tinking to start/: {{{ s      Log On


   

Question 544592: simplify the fractional expression:
+sqrt%281%2B%28x%5E3+-+1%2F4x%5E3%29%5E2%29
This is the last question i have in this section an stumped on where to start. Tinking to start/:
+sqrt%281%2B%28x%5E6+-+1%2F4x%5E6%29%29
--
then
+sqrt%281%2B%28x%5E6%284x%5E6%29%2F4x%5E6+-+1%2F4x%5E6%29%29
--
next
simplify:
+sqrt%281%2B%284x%5E9+-+1%29%2F4x%5E6%29%29
---
+sqrt%284x%5E6%2F4x%5E6+%2B+%284x%5E9+-+1%29%2F4x%5E6%29%29
--
+sqrt%28%284x%5E6+%2B+4x%5E9+-+1%29%2F4x%5E6%29%29
---
What next?
Found 2 solutions by friesr, JBarnum:
Answer by friesr(113) About Me  (Show Source):
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!

+sqrt%281%2B%28x%5E3+-+1%2F%284x%5E3%29%29%5E2%29
+sqrt%281%2B%28x%5E3+-+1%2F%284x%5E3%29%29%28x%5E3+-+1%2F%284x%5E3%29%29%29


+sqrt%281%2B+x%5E6+-+2%2F%284%29+%2B+1%2F%2816x%5E6%29%29%29
+sqrt%281%2B+x%5E6+-+1%2F2+%2B+1%2F%2816x%5E6%29%29%29
+sqrt%28x%5E6+%2B+1%2F2+%2B+1%2F%2816x%5E6%29%29%29 i dont like fractions so i get rid of denominators by multiplying by a 1/1 from the greatest denomonator

+sqrt%28%2816x%5E12+%2B+8x%5E6+%2B+1%29%2F%2816x%5E6%29%29
+sqrt%28%28%2816x%5E12+%2B+4x%5E5+%2B+4x+%2B+1%29%29%2F%2816x%5E6%29%29%29%29
+sqrt%28%284x%5E5%284x%5E7+%2B+1%29+%2B+1%284x+%2B+1%29%29%2F%2816x%5E6%29%29%29
+sqrt%28%28%284x%5E5%2B1%29%284x%5E7+%2B+1%29%284x+%2B+1%29%29%2F%2816x%5E6%29%29%29
thats as far as i know how to go