Square Roots and other things to simplify

**Harryhit4** · September 16th 2007, 04:16 PM

I've started accelerated geometry now, in 8th grade, and an algebra review packet is due. I really need help to remember how to do problems like -

[square root of] 48rs^3

[square root of]63 + [square root of]28 - [square root of]1/7

3[square root of]5x
------------------- (over)
5[square root of]6y

x^2 + 2x + 1
----(over)
3x
-------------(all over)
x+1
----(over)
2x

Sorry, I didn't know how to use the math tags. I hope you will be able to read it.

Could someone please solve these and then show me how they did it?

**TKHunny** · September 16th 2007, 07:02 PM

Originally Posted by Harryhit4

[square root of] 48rs^3

Pull out all the square things.

$48 = 3*16 = 3*4^{2}$

$s^{3} = s*s^{2}$

So, $\sqrt{48rs^{3}} = 4|s|\sqrt{3rs}$

**Harryhit4** · September 17th 2007, 03:39 PM

Originally Posted by TKHunny

Pull out all the square things.

$48 = 3*16 = 3*4^{2}$

$s^{3} = s*s^{2}$

So, $\sqrt{48rs^{3}} = 4|s|\sqrt{3rs}$

Thanks, can anyone else help me with the others?

**topsquark** · September 18th 2007, 05:21 AM

Originally Posted by Harryhit4

x^2 + 2x + 1
----(over)
3x
-------------(all over)
x+1
----(over)
2x

The LCM of 3x and 2x is 6x, so you multiply the fraction by $\frac{6x}{6x} = 1$ , which does not change the value.

$\frac{ \frac{x^2 + 2x + 1}{3x} }{ \frac{x + 1}{2x} }$

$= \frac{ \frac{x^2 + 2x + 1}{3x} }{ \frac{x + 1}{2x} } \cdot \frac{6x}{6x};~x \neq 0$

$= \frac{ \frac{x^2 + 2x + 1}{3x} \cdot 6x}{ \frac{x + 1}{2x} \cdot 6x};~x \neq 0$

$= \frac{2(x^2 + 2x + 1)}{3(x + 1)};~x \neq 0$

Now do some factoring:
$= \frac{2(x + 1)^2}{3(x + 1)};~x \neq 0$

$= \frac{2(x + 1)}{3};~x \neq -1,0$

-Dan

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