Quadratic formula problem.

[Whitcomb]

I'm having some trouble following a process that's laid out in the book I'm working through.



Specifically on step 3 I'm not understanding how eliminating the -10 on the bottom is seemingly dividing the -30 by -10, but also dividing the 20 by positive 100 and the 30^2 by positive 10.

 

[tkhunny]

Fair enough. It does appear to have skipped a thing or two.

1) Factor the terms under the radical by identifying factors of 10^2.
2) Bring the 10^2 factors outside the radical. Example: \(\displaystyle \sqrt{3\cdot 10^{2} + 5\cdot 10^{2}} = 10\cdot\sqrt{3+ 5}\)
3) Find the common factor of 10 in ALL terms, numerator and denominator.

That's where it picks up in the next step.

 

[mmm4444bot]

Dividing by -10 is the same as multiplying by -1/10.

\(\displaystyle -\dfrac{1}{10} \text{ may be written as } -\mspace{-5mu}\sqrt{\dfrac{1}{100}}\)

There is also this property of radicals:

\(\displaystyle \sqrt{m} \cdot \sqrt{n} = \sqrt{m \cdot n}\)

All of this leads to the 30^2 and 20 (in the radicand) being divided by 100.

 

[Whitcomb]

Fair enough. It does appear to have skipped a thing or two.

1) Factor the terms under the radical by identifying factors of 10^2.
2) Bring the 10^2 factors outside the radical. Example: \(\displaystyle \sqrt{3\cdot 10^{2} + 5\cdot 10^{2}} = 10\cdot\sqrt{3+ 5}\)
3) Find the common factor of 10 in ALL terms, numerator and denominator.

That's where it picks up in the next step.

Okay, I think I'm getting on the right track, but the 3 i still throwing me off.

So in the √ I have:
sqrt(30^2 +20(60 - h))

sqrt(3*10^2 + .2*10^2(60 - h))

10sqrt(3 + .2(60 - h))

Now I'm just not clear on why the 3 is still squared after.

 

[tkhunny]

30^2 = (3*10)^2 = 3^2 * 10^2

 

[Whitcomb]

Oh boy, I feel silly after that one.

Thanks for the help guys!