MHB Calculating (125 2/3)^2: 3-Square-Root-of-5

[CSmith1]

1) 125 2/3(125 1/3)^2

=( 3 square root 125)^2
=(3 square root 5x5x5)^2
=(3 square root 5 )^2 right so far?

 

[Jameson]

1) 125 2/3(125 1/3)^2

=( 3 square root 125)^2
=(3 square root 5x5x5)^2
=(3 square root 5 )^2 right so far?

Looks correct to me. Why don't you try solving a few problems fully and post them all at once to make this more efficient? :) It's better to type too much than not enough with online math help.

Good job by the way on learning this stuff!

 

[CSmith1]

OK.



CONTINUED

3 SQUARE ROOT 5 X 3 SQUARE ROOT 5
=9(5 SQUARE ROOT 5)
= 25 square root 5

 

[Jameson]

OK.

CONTINUED

3 SQUARE ROOT 5 X 3 SQUARE ROOT 5
=9(5 SQUARE ROOT 5)
= 25 square root 5

You got part of it right. The 3's will combine into 9 so now you must calculate the square root bits. After multiplying 3*3 you have [math]\sqrt{5} \cdot \sqrt{5}[/math] remaining, which is multiplied together. A common fact that is useful in these problems is that squaring and taking the square root are opposite operations, so when you do both to one number, nothing happens.

[math]\sqrt{5} \cdot \sqrt{5}=( \sqrt{5})^2=5[/math]

Now what do you get for your answer?

 

[Sudharaka]

1) 125 2/3(125 1/3)^2

=( 3 square root 125)^2
=(3 square root 5x5x5)^2
=(3 square root 5 )^2 right so far?

Hi CSmith, :)

Note that, \((\sqrt[3]{5\times 5\times 5})^2=5^2\). But you have written, \((\sqrt[3]{5\times 5\times 5})^2=(\sqrt[3]{5})^2\) which is incorrect.

Kind Regards,
Sudharaka.

 

[Sudharaka]

Hi CSmith, :)

I went through most of your posts and it seems to me that you are making a lot of effort to typeset the mathematics in them. I suggest you to learn a bit of LaTeX commands. It's very easy. :) For starters, you can read the http://www.mathhelpboards.com/f26/ section.

As an example let me show you how to typeset your question in LaTeX.

\[125^{\frac{2}{3}}=(125^{\frac{1}{3}})^2\]

\[=(\sqrt[3]{125})^2\]

\[=(\sqrt[3]{5\times 5\times 5})^2\]

\[=(\sqrt[3]{5})^2\]

This will produce,

\[125^{\frac{2}{3}}=(125^{\frac{1}{3}})^2\]

\[=(\sqrt[3]{125})^2\]

\[=(\sqrt[3]{5\times 5\times 5})^2\]

\[=(\sqrt[3]{5})^2\]

To make the equal signs align with each other you can use the "eqnarray" environment as follows,

\begin{eqnarray}

125^{\frac{2}{3}}&=&(125^{\frac{1}{3}})^2\\

&=&(\sqrt[3]{125})^2\\

&=&(\sqrt[3]{5\times 5\times 5})^2\\

&=&(\sqrt[3]{5})^2

\end{eqnarray}

will give you,

\begin{eqnarray}

125^{\frac{2}{3}}&=&(125^{\frac{1}{3}})^2\\

&=&(\sqrt[3]{125})^2\\

&=&(\sqrt[3]{5\times 5\times 5})^2\\

&=&(\sqrt[3]{5})^2

\end{eqnarray}

Kind Regards,
Sudharaka.