# Math Help - Simplifying expressions

1. ## Simplifying expressions

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

2. 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

3. ## Thanks

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))

4. 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

5. 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.

6. Is this alright for

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

3 sqrt (3)

7. Originally Posted by Nash55
Is this alright for

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

3 sqrt (3)