Friday, 28 February 2014

Simplify the following. ˆš(128x^6)+ˆš(98x^6)

When
you see problems like this, go to the instructions to see if there are restrictions on what `x`
can be. Most books I've seen specify that all variables are non-negative, for the following
reason.

Let `x=-3.` You'll find that `sqrt(128x^6)+sqrt(98x^6)=405sqrt(2),`

while `15x^3sqrt(2)=-405sqrt(2),`

so the expressions are
not equal. The reason is that `sqrt(x^6)=x^3` is not true if `x` is negative. What is
true
for all values of `x` is that `sqrt(x^6)=|x|^3,` but I guess constantly having
to write things like `15|x|^3sqrt(2)` (or...

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