Simplifying expressions

**Nash55** · December 3rd 2007, 10:11 AM

If someone could tell me how to express the square root of something, I'll quickly put the problems up here. Thanks.

**topsquark** · December 3rd 2007, 10:25 AM

Originally Posted by Nash55

If someone could tell me how to express the square root of something, I'll quickly put the problems up here. Thanks.

Well, I would express the square root of 23 as $\sqrt{23}$ . If it's the coding you are looking for, just click on the nice-looking expression. Otherwise you can write "sqrt(23)" and we'll all know what it means.

-Dan

**Nash55** · December 3rd 2007, 10:40 AM

If you could help simplifying these expressions, and showing the work, that'd be great. Thanks.

^3 sqrt(54x^4)

sqrt(32x^5)

sqrt(5x) multiplied by ^3 sqrt(5x)

5 sqrt (3) + 2 sqrt(12) - 2 sqrt(27)

( 4 sqrt (2) – sqrt (3) ) ( 5 sqrt (2) + 2 sqrt (3))

**topsquark** · December 3rd 2007, 10:58 AM

Originally Posted by Nash55

^3 sqrt(54x^4)

$\sqrt[3]{54x^4} = \sqrt[3]{27x^3 \cdot 2x}$

$= \sqrt[3]{27x^3} \cdot \sqrt[3]{2x}$

$= \sqrt[3]{3^3x^3} \cdot \sqrt[3]{2x}$

$= 3x \sqrt[3]{2x}$

Try grouping the radicand like I did above.

-Dan

**earboth** · December 3rd 2007, 11:02 AM

Originally Posted by Nash55

If you could help simplifying these expressions, and showing the work, that'd be great. Thanks.

^3 sqrt(54x^4)

sqrt(32x^5)

sqrt(5x) multiplied by ^3 sqrt(5x)

5 sqrt (3) + 2 sqrt(12) - 2 sqrt(27)

( 4 sqrt (2) – sqrt (3) ) ( 5 sqrt (2) + 2 sqrt (3))

Hello,

I'm just guessing. I assume that you mean:

$\sqrt[3]{54x^4}=\sqrt[3]{27x^3 \cdot 2x}=3x \cdot \sqrt[3]{2x}$

$\sqrt{32x^5}=\sqrt{16x^4 \cdot 2x}= 4x^2 \cdot \sqrt{2x}$

With the next problem it's easiest if you use powers:

$\sqrt{5x} \cdot \sqrt[3]{5x}=(5x)^{\frac12} \cdot (5x)^{\frac13}=(5x)^{\frac12 + \frac13}=(5x)^{\frac56}$

I'll leave the rest for you.

**Nash55** · December 3rd 2007, 12:26 PM

Is this alright for

5 sqrt (3) + 2 sqrt (12) - 2 sqrt (27)=

3 sqrt (3)

**topsquark** · December 3rd 2007, 02:42 PM

Originally Posted by Nash55

Is this alright for

5 sqrt (3) + 2 sqrt (12) - 2 sqrt (27)=

3 sqrt (3)

The answer is "yes."

(Hmmmm... As you asked me this in a PM, this could be considered a double post...)

-Dan

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