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

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 $\displaystyle{x}$
can be. Most books I've seen specify that all variables are non-negative, for the following
reason.

Let $\displaystyle{x}=-{3}.$ You'll find that $\displaystyle\sqrt{{{128}{{x}}^{{6}}}}+\sqrt{{{98}{{x}}^{{6}}}}={405}\sqrt{{{2}}},$

while $\displaystyle{15}{{x}}^{{3}}\sqrt{{{2}}}=-{405}\sqrt{{{2}}},$

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

Notes

Friday, 28 February 2014

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

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